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NASA NTRS1972

Pioneer 7 observations of the August 29, 1966, interplanetary shock-wave ensemble.

The detailed plasma (except for electrons) and magnetic field data from Pioneer 7 are presented for a proposed double-shock ensemble. The Ames Research Center plasma probe data are compared with that of the MIT probe. These data are compared with MHD theory to show that the discontinuities themselves satisfy the magnetic Hugoniot equations. The data are also compared with the theoretical predictions for the double-shock structure. The theory requires as input only the forward shock velocity, the original ambient solar wind conditions, and a reasonable assumption regarding the density and azimuthal magnetic field in the 'new' solar wind which is detected after passage of the reverse shock. A unique solution is then obtained for the theoretical piston and reverse shock positions as well as for the temporal plasma behavior for both infinite and finite electrical conductivities.

Dryer, M.↗

NASA NTRS2009

Simulation of an Isolated Tiltrotor in Hover with an Unstructured Overset-Grid RANS Solver

An unstructured overset-grid Reynolds Averaged Navier-Stokes (RANS) solver, FUN3D, is used to simulate an isolated tiltrotor in hover. An overview of the computational method is presented as well as the details of the overset-grid systems. Steady-state computations within a noninertial reference frame define the performance trends of the rotor across a range of the experimental collective settings. Results are presented to show the effects of off-body grid refinement and blade grid refinement. The computed performance and blade loading trends show good agreement with experimental results and previously published structured overset-grid computations. Off-body flow features indicate a significant improvement in the resolution of the first perpendicular blade vortex interaction with background grid refinement across the collective range. Considering experimental data uncertainty and effects of transition, the prediction of figure of merit on the baseline and refined grid is reasonable at the higher collective range- within 3 percent of the measured values. At the lower collective settings, the computed figure of merit is approximately 6 percent lower than the experimental data. A comparison of steady and unsteady results show that with temporal refinement, the dynamic results closely match the steady-state noninertial results which gives confidence in the accuracy of the dynamic overset-grid approach.

Lee-Rausch, Elizabeth M.↗

NASA NTRSDate not supplied

Trade-Offs of Simplified Versus Comprehensive Representation of Mineralogy When Studying Dust Impacts on Earth’s Climate Systems

The intensity and direction of dust impacts on Earth’s climate systems depend on mineral composition. For example, the presence or absence of a few percent of iron oxides in dust will determine if dust is warming or cooling the atmosphere. Similarly, feldspar will enhance ice cloud formation, while acid gases in the atmosphere will react on the surface of dust calcite limiting acid rain. Still, most climate models use a simplified representation of dust mineralogy. They assume a fixed composition at emission which stays invariant during transport and removal. Such simplification assumes spatially and temporally constant physical and chemical properties of dust, and appears to provide satisfactory results when comparing some properties with observations. The trade-off is their lack of spatial gradients, which will fail to induce circulation, cloud and precipitation changes. The two reasons to omit mineral variations are the uncertainty of current atlases of soil mineral composition in arid regions, and, more practically, an improved runtime efficiency. The former reason is losing ground with the recent launch (July 2022) of a dedicated mission (NASA/JPL EMIT) to retrieve global soil mineralogy of dust sources at high spatial resolution. While the EMIT science team is finalizing a satisfactory global map of mineral composition of dust sources, we analyzed the interaction of dust mineralogy on radiation and its impact on the fast temperature response using different representations of mineral composition from detailed and spatially varying to simplified and globally uniform, assuming different hematite contents and methods to calculate optical properties. Our results show that resolving dust mineralogy reduces dust absorption, and results in improved agreement with observation-based single scattering albedo (SSA), radiative fluxes from CERES (the Clouds and the Earth’s Radiant Energy System), and land surface temperature from CRU (Climatic Research Unit), compared to the baseline bulk dust model version. It also results in distinct radiative impacts on Earth’s climate over North Africa. From our 19-year simulation, we will show that it leads to a reduction of over 50% in net downward radiation at top of atmosphere (TOA) across the Sahara and an approximately 20% reduction over the Sahel. We will explain how the surface temperature response affects the monsoon flow from the Gulf of Guinea. Interestingly, we find similar results by simply fixing the hematite content of dust to a globally uniform value of 0.9% by volume. We will discuss the underlying reasons for such results and show that they may be unrelated to the distribution of soil mineralogy. Still, an accurate representation of soil mineralogy is necessary to better understand dust impacts on the Earth’s climate systems.

dust impacts↗

DOE OSTI2025

SNoGloDe: A Structured Nonlinear Global Decomposition Solver

Large-scale optimization problems often require decomposition strategies and customized algorithms to achieve optimal solutions within a reasonable time. Building on the work of Cao and Zavala (2019) for solving nonlinear two-stage stochastic programs to global optimality, we implement and extend their approach. We generalize to optimization problems reformulated with a block-angular constraint structure (e.g., temporal decomposition). Our framework, written in Python using Pyomo, is highly customizable and enables parallel execution of the decomposition. SNoGloDe allows tailored branching strategies, lower bounding problems, and candidate generators to leverage problem-specific knowledge. To demonstrate effectiveness, we compare SNoGloDe’s performance with Gurobi on a temporally decomposed produced water case study.

algorithms↗

NASA NTRS1973

Electric fields and plasma convection in the plasmasphere.

A review is given of present theoretical and experimental information on quasistatic electric fields in and near the plasmasphere with the aim of discussing plasma flow within the plasmasphere, dynamo electric fields, and the penetration of electric fields of magnetospheric origin to low latitudes. Data are presented that suggest that the mean temporal variation of electric fields at all latitudes is diurnal, that dynamo electric fields are more important near L = 3 and are less important near and beyond L = 4 than are fields of magnetospheric origin, and that magnetospheric fields with periods that are a reasonable fraction of one day efficiently penetrate the plasmapause.

Mozer, F. S.↗

NASA NTRS2003

Lightning and Other Influences On Tropical Tropospheric Ozone: Empirical Studies of Covariation

Tropical and subtropical tropospheric ozone are important radiatively active species, with particularly large effects in the upper third of the troposphere. Temporal variability of O3 has proved difficult to simulate day by day in process models. Thus, individual roles of lightning, biomass burning, and other pollution in providing precursor NO(x), radicals, and chain carriers (CO, hydrocarbons) remain unquantified by simulation, and it is theoretically reasonable that individual roles are magnified by a joint synergy. We use wavelet analysis and Burg-algorithm maximum entropy spectral analyses to describe time-scales and correlation of ozone with proxies for processes controlling its concentration. Our empirical studies link time variations apparent in several datasets: the SHADOZ (Southern Hemisphere Additional Ozonesondes) network stations (Nairobi, Fiji), and auxiliary series with power to explain ozone-determining processes, with some interpretation based on the TTO (Tropical Tropospheric Ozone) product derived from TOMS (the Total Ozone Mapping Spectrometer). The auxiliary series are The OTD/LIS(Optical Transient Detector/Lightning Imaging Sensor) measurements of the lightning NO(x) source, the OLR (Outgoing Longwave Radiation)measurement of high-topped clouds, and standard meteorological variables from the United States NCEP (National Centers for Environmental Prediction) and Data Assimilation Office analyses. Concentrating on equatorial ozone, we compare the statistical evidence on the variability of tropospheric ozone. Important variations occur on approximately two-week, two-month (Madden-Julian Oscillation) and annual scales, and relations with OLR suggest controls associated with continental clouds. Hence we are now using the Lightning Imaging Sensor data set to indicate NO(x) sources. We report initial results defining relative roles of the process mentioned affecting O3 using their covariance properties.

Chatfield, Robert B.↗

NASA NTRS1980

Investigations of eddy coherence in jet flows

In turbulent shear flow the term coherent structures refers to eddies which are both spatially coherent, i.e., large eddies, aand also temporally coherent, i.e., they retain their identities for times which are long compared with their time scales in fixed point measurements. In transitional flows, the existence of such structures is evident from flow visualizations. In many other flows, such structures are not so evident. The reasons for the existence of these two classes of flows are discussed and attention is focused upon the more difficult flows, where coherent structures are not so evident. Techniques by which the existence (or nonexistence) of such structures in these flows can be established from point measurements, are also discussed. A major problem is shown to be the need to discriminate between real losses in eddy coherence and apparent losses in coherence introduced by phase scrambling effects which 'smear' multipoint correlations. The analysis of multiprobe time dependent data in cold and reacting round turbulent jets is described and it is shown how evidence of strong eddy coherence can be extracted from data.

Yule, A. J.↗

NASA NTRS1990

N-Decane-Air Droplet Combustion Experiments in the NASA-Lewis 5 Second Zero-Gravity Facility

The burning of single fuel (n-decane) droplets in a microgravity environment (below 0.00001 of the earth's gravity, achieved in the NASA-Lewis 5-Second Zero-Gravity Facility) was studied, as part of the development of the Droplet Combustion Experiment for eventual operation aboard either the Shuttle middeck or Spacelab. Special attention is given to the combustion equipment used and its operations and performance. Temporal analysis of the local burning rates in these tests showed increasing rates of change in the local burning as droplet combustion progressed. Result point to the need of studying large droplets, with long droplet combustion lifetimes as well as low gas/droplet motion to understand reasons for this unsteadiness.

Haggard, John B.↗

NASA NTRS2000

Sensitivity of Spacebased Microwave Radiometer Observations to Ocean Surface Evaporation

Ocean surface evaporation and the latent heat it carries are the major components of the hydrologic and thermal forcing on the global oceans. However, there is practically no direct in situ measurements. Evaporation estimated from bulk parameterization methods depends on the quality and distribution of volunteer-ship reports which are far less than satisfactory. The only way to monitor evaporation with sufficient temporal and spatial resolutions to study global environment changes is by spaceborne sensors. The estimation of seasonal-to-interannual variation of ocean evaporation, using spacebased measurements of wind speed, sea surface temperature (SST), and integrated water vapor, through bulk parameterization method,s was achieved with reasonable success over most of the global ocean, in the past decade. Because all the three geophysical parameters can be retrieved from the radiance at the frequencies measured by the Scanning Multichannel Microwave Radiometer (SMMR) on Nimbus-7, the feasibility of retrieving evaporation directly from the measured radiance was suggested and demonstrated using coincident brightness temperatures observed by SMMR and latent heat flux computed from ship data, in the monthly time scale. However, the operational microwave radiometers that followed SMMR, the Special Sensor Microwave/Imager (SSM/I), lack the low frequency channels which are sensitive to SST. This low frequency channels are again included in the microwave imager (TMI) of the recently launched Tropical Rain Measuring Mission (TRMM). The radiance at the frequencies observed by both TMI and SSM/I were simulated through an atmospheric radiative transfer model using ocean surface parameters and atmospheric temperature and humidity profiles produced by the reanalysis of the European Center for Medium Range Weather Forecast (ECMWF). From the same ECMWF data set, coincident evaporation is computed using a surface layer turbulent transfer model. The sensitivity of the radiance to evaporation over various seasons and geographic locations are examined. The microwave frequencies with radiance that are significant correlated with evaporation are identify and capability of estimating evaporation directly from TMI will be discussed.

Liu, Timothy W.↗

NASA NTRS2012

Intercomparison of Desert Dust Optical Depth from Satellite Measurements

This work provides a comparison of satellite retrievals of Saharan desert dust aerosol optical depth (AOD) during a strong dust event through March 2006. In this event, a large dust plume was transported over desert, vegetated, and ocean surfaces. The aim is to identify the differences between current datasets. The satellite instruments considered are AATSR, AIRS, MERIS, MISR, MODIS, OMI, POLDER, and SEVIRI. An interesting aspect is that the different algorithms make use of different instrument characteristics to obtain retrievals over bright surfaces. These include multi-angle approaches (MISR, AATSR), polarisation measurements (POLDER), single-view approaches using solar wavelengths (OMI, MODIS), and the thermal infrared spectral region (SEVIRI, AIRS). Differences between instruments, together with the comparison of different retrieval algorithms applied to measurements from the same instrument, provide a unique insight into the performance and characteristics of the various techniques employed. As well as the intercomparison between different satellite products, the AODs have also been compared to co-located AERONET data. Despite the fact that the agreement between satellite and AERONET AODs is reasonably good for all of the datasets, there are significant differences between them when compared to each other, especially over land. These differences are partially due to differences in the algorithms, such as assumptions about aerosol model and surface properties. However, in this comparison of spatially and temporally averaged data, it is important to note that differences in sampling, related to the actual footprint of each instrument on the heterogeneous aerosol field, cloud identification and the quality control flags of each dataset can be an important issue.

desert dust↗

NASA NTRS1998

Modeling Macro- and Micro-Scale Turbulent Mixing and Chemistry in Engine Exhaust Plumes

Simulation of turbulent mixing and chemical processes in the near-field plume and plume-vortex regimes has been successfully carried out recently using a reduced gas phase kinetics mechanism which substantially decreased the computational cost. A detailed mechanism including gas phase HOx, NOx, and SOx chemistry between the aircraft exhaust and the ambient air in near-field aircraft plumes is compiled. A reduced mechanism capturing the major chemical pathways is developed. Predictions by the reduced mechanism are found to be in good agreement with those by the detailed mechanism. With the reduced chemistry, the computer CPU time is saved by a factor of more than 3.5 for the near-field plume modeling. Distributions of major chemical species are obtained and analyzed. The computed sensitivities of major species with respect to reaction step are deduced for identification of the dominant gas phase kinetic reaction pathways in the jet plume. Both the near field plume and the plume-vortex regimes were investigated using advanced mixing models. In the near field, a stand-alone mixing model was used to investigate the impact of turbulent mixing on the micro- and macro-scale mixing processes using a reduced reaction kinetics model. The plume-vortex regime was simulated using a large-eddy simulation model. Vortex plume behind Boeing 737 and 747 aircraft was simulated along with relevant kinetics. Many features of the computed flow field show reasonable agreement with data. The entrainment of the engine plumes into the wing tip vortices and also the partial detrainment of the plume were numerically captured. The impact of fluid mechanics on the chemical processes was also studied. Results show that there are significant differences between spatial and temporal simulations especially in the predicted SO3 concentrations. This has important implications for the prediction of sulfuric acid aerosols in the wake and may partly explain the discrepancy between past numerical studies (that employed parabolic or temporal approximations) and the measured data. Finally to address the major uncertainty in the near-field plume modeling related to the plume processing of sulfur compounds and advanced model was developed to evaluate its impact on the chemical processes in the near wake. A comprehensive aerosol model is developed and it is coupled with chemical kinetics and the axisymmetric turbulent jet flow models. The integrated model is used to simulate microphysical processes in the near-field jet plume, including sulfuric acid and water binary homogeneous nucleation, coagulation, non-equilibrium heteromolecular condensation, and sulfur-induced soot activation. The formation and evolution of aerosols are computed and analyzed. The computed results show that a large number of ultra-fine (0.3--0.6 nm in radius) volatile HSO4 - HO embryos are generated in the near-field plume. These embryos further grow in size by self coagulation and condensation. Soot particles can be activated by both heterogeneous nucleation and scavenging of H2SO4-H2O aerosols. These activated soot particles can serve as water condensation nuclei for contrail formation. Conditions under which ice contrails can form behind aircrafts are studied. The sensitivities of the threshold temperature for contrail formation with respect to aircraft propulsion efficiency, relative humidity, and ambient pressure are evaluated. The computed aerosol properties for different extent of fuel sulfur conversion to S(VI) (SO3 and H2SO4) in engine are examined and the results are found to be sensitive to this conversion fraction.

Menon, Suresh↗

NASA NTRS2012

Desert Dust Satellite Retrieval Intercomparison

This work provides a comparison of satellite retrievals of Saharan desert dust aerosol optical depth (AOD) during a strong dust event through March 2006. In this event, a large dust plume was transported over desert, vegetated, and ocean surfaces. The aim is to identify and understand the differences between current algorithms, and hence improve future retrieval algorithms. The satellite instruments considered are AATSR, AIRS, MERIS, MISR, MODIS, OMI, POLDER, and SEVIRI. An interesting aspect is that the different algorithms make use of different instrument characteristics to obtain retrievals over bright surfaces. These include multi-angle approaches (MISR, AATSR), polarisation measurements (POLDER), single-view approaches using solar wavelengths (OMI, MODIS), and the thermal infrared spectral region (SEVIRI, AIRS). Differences between instruments, together with the comparison of different retrieval algorithms applied to measurements from the same instrument, provide a unique insight into the performance and characteristics of the various techniques employed. As well as the intercomparison between different satellite products, the AODs have also been compared to co-located AERONET data. Despite the fact that the agreement between satellite and AERONET AODs is reasonably good for all of the datasets, there are significant differences between them when compared to each other, especially over land. These differences are partially due to differences in the algorithms, such as as20 sumptions about aerosol model and surface properties. However, in this comparison of spatially and temporally averaged data, at least as significant as these differences are sampling issues related to the actual footprint of each instrument on the heterogeneous aerosol field, cloud identification and the quality control flags of each dataset.

Carboni, E.↗

NASA NTRSDate not supplied

WMLES of Boundary-Layer Transition

An analysis of the potential for the accurate prediction of laminar-turbulent transition by Wall-Modeled Large-Eddy Simulation (WMLES) indicates that satisfactory prediction of transition by WMLES is possible, provided a) a sufficiently accurate wall model for the initial stage of transition is employed, b) a satisfactory transition is made between this initial-stage wall model and the wall model for the downstream fully-developed turbulence, and c) limitations on temporal and spatial resolution, and on the thickness of the wall-modeled region, imposed by the need to accurately resolve the disturbance waves and the transition region are observed. This is illustrated with WMLES computations of subharmonic transition in a flat-plate boundary layer that yield reasonable agreement with DNS results. However, the wall-modeled region thickness, and thus the cost savings, is less than is typical for WMLES of fully developed turbulence.

wall-modeled large-eddy simulation↗

NASA NTRSDate not supplied

WMLES of Boundary-Layer Transition

Wall-modeled large-eddy simulation↗

NASA NTRS1975

A new global ionospheric model

A new global ionospheric model has been successfully implemented. The daytime portion of this model provides one-way ionospheric range corrections that compare favorably with those derived from the Mariner Venus Mercury (MVM'73) S- and X-band dual frequency doppler data. For elevation angles, γ, higher than 30 deg and solar zenith angle, X, less than 80 deg, this model provides calibrations accurate to a few centimeters. The calibrations provided by the nighttime model are also very reasonable. These, however, will have to be compared with the S/X data from Viking ‘75 for final confirmation. It is interesting to note that the daytime ionospheric calibrations derived from the current calibration scheme, DIEN/TIEN, are fairly close to those given by the new global model, especially in the temporal variations and thus the doppler effects. In the daytime and for γ ≳ 30 deg and X < 80 deg, the calibrations from the two models agree almost exactly. However, for situations when γ is below 30 deg and X is larger than 80 deg simultaneously, as much as 12% (~70 cm, typically) improvement of the new model over DIEN/TIEN results. The comparison between the nighttime model and DIEN/TIEN has been based on the one-way ionospheric range corrections for three passes near the Mariner 9 encounter with Mars in 1971 tracked at Goldstone. It is found that they can differ by over 30% (typically 20 cm). As mentioned, the confirmation of these nighttime calibrations awaits the availability of the Viking S/X dual frequency doppler data. Finally, the ionospheric calibration effects on orbit determination provided by DIEN/TIEN, the global model, and the S/X data will be intercompared during the Viking Mission.

K. W. Yip↗

NASA NTRS1993

Direct simulation of compressible wall-bounded turbulence

When analyzing many turbulent flows, the effects of compressibility can be neglected. Even some relatively high-speed flows, such as boundary layers generated by a supersonic aircraft, produce turbulent statistics that are similar to those found for the incompressible case. There are other situations, however, in which the non-zero divergence of the turbulence leads to behavior that is fundamentally different from that found at constant density. Examples include flows created by internal combustion engines, hypersonic flight, and supersonic combustion. It is with instances such as these that this project is concerned. In particular, we are interested in the effects of compressibility on turbulence near a smooth solid constant temperature surface; our primary objective is an increased physical understanding that can be used to improve turbulence models of wall-bounded compressible flows. With this in mind, we have begun a direct numerical simulation (DNS) study of turbulence in a plane channel. Because all of the relevant spatial and temporal scales are to be resolved, the simulations require no subgrid scale parameterization. The DNS code developed by Buell to study compressible plane Couette flow was modified to solve the compressible Navier-Stokes equations in the plane channel. The channel was chosen over the Couette flow for two reasons: (1) to avoid using the very large streamwise domains needed to adequately capture the large Couette vortical structures; and (2) to make use of previous experience by considering the compressible version of a well established case and isolate finite Mach number effects by comparing to the incompressible channel.

Coleman, Gary N.↗

NASA NTRS1998

Guest Investigator Studies with the Compton Gamma Ray Observatory

The cumulative all-sky survey by the Compton Gamma Ray Observatory (CGRO), composed of data acquired during the first three years of the mission, included a number of regions of very limited exposure. The most glaring deficiency in coverage was toward the region of the South Galactic Pole (SGP), which received significantly less exposure than other directions- by a factor of at least 2 to 3. Furthermore, nearly all of the SGP exposure was accumulated during the first year of the mission. Since blazars are known to be time-variable, and of unknown duty cycle, a pointing of the CCRO in that direction was considered highly desirable, and long overdue. In addition, data gathered from a pointing toward the SGP and its comparison with comprehensive data available for the North Galactic Pole would be extremely valuable to investigators studying the extragalactic diffuse emission. The reasons outlined above prompted our initiation of a Cycle 4 campaign to systematically search with EGRET and COMPTEL for gamma-ray emission from sources near the South Galactic Pole. The Cycle 4 SGP campaign consisted of tnvo 14-day observations separated in in time by approximately 10 months. The temporal separation of the observations was requested to allow a test for possible variations in the detected sources. Our primary targets were 38 FSRQs which lie within 30 degrees of the SGP, and which satisfy the basic criteria for candidate gamma-ray AGNs,flat-spectrum radio sources, many of which exhibit blazar-type properties). These targets were selected from the standard references, and from the available on-line databases (e.g., the NASA Extragalactic Database, NED), as the most promising AGN targets in the vicinity of the SGP. A 30 radius from the SGP was chosen as the boundary of our survey, since the selected targets would then fall within the most sensitive portion of the fields of view of EGRET and COMPTEL (i.e., within a 30 zenith angle), for a CGRO pointing directed exactly at the SGP. Our South Galactic Pole Survey yielded a number of exciting results. The EGRET data were analyzed using the maximum likelihood techniques to estimate the intensity, spectrum, and position of gamma-ray sources in the field of view. Our analysis revealed four sources at energies greater than 100 MeV with likelihood ratios corresponding to greater than 30 detections (Vestrand et al. 1996). One of the sources is associated with the well known gamma-ray blazar PKS 0208-512, but the other three were previously unknown. Among the new detections was PKS 2155-304 which is often considered a prototype of the x-ray selected BL Lacs. PKS 2155-304, which was also detected at hard x-ray energies by CGRO/OSSE, is one of the brightest BL Lac objects in the sky at optical through x-ray energies and has a history of rapid, strong multiwavelength variability. As such, it has been the subject of intensive, contemporaneous, multiwavelength monitoring covering radio frequencies to x-ray energies.

Vestrand, W. T.↗

NASA NTRS2000

A Regional-Scale Assessment of Satellite Derived Precipitable Water Vapor Across The Amazon Basin

Atmospheric water vapor is widely recognized as a key climate variable, linking an assortment of poorly understood and complex processes. It is a major element of the hydrological cycle and provides a mechanism for energy exchange among many of the Earth system components. Reducing uncertainty in our current knowledge of water vapor and its role in the climate system requires accurate measurement, improved modeling techniques, and long-term prediction. Satellites have the potential to satisfy these criteria, as well as provide high resolution measurements that are not available from conventional sources. The focus of this paper is to examine the temporal and mesoscale variations of satellite derived precipitable water vapor (PW) across the Amazon Basin. This region is pivotal in the functioning of the global climate system through its abundant release of latent heat associated with heavy precipitation events. In addition, anthropogenic deforestation and biomass burning activities in recent decades are altering the conditions of the atmosphere, especially in the planetary boundary layer. A physical split-window (PSW) algorithm estimates PW using images from the GOES satellites along with the NCEP/NCAR Reanalysis data that provides the first guess information. Retrievals are made at a three-hourly time step during daylight hours in the Amazon Basin and surrounding areas for the months of June and October in 1988 (dry year) and 1995 (wet year). Spatially continuous fields are generated 5 times daily at 12Z, 15Z, 18Z, 21Z, and 00Z. These fields are then averaged to create monthly and 3 hourly monthly grids. Overall, the PSW estimates PW reasonable well in the Amazon with MAE ranging from 3.0 - 9.0 mm and MAE/observed mean around 20% in comparison to radiosonde observations. The distribution of PW generally mimics that of precipitation. Maximum values (42 - 52 mm) are located in the Northwest whereas minimum values (18 - 27 mm) are found along Brazil's East coast. Aside from the East coast, PW has a stronger north-south gradient than that of rainfall. As for the temporal variation of PW, June (1988 and 1995) experiences a peak about 1400 local time, corresponding to a maximum in air temperature. In contrast, October (1988 and 1995) experiences a maximum early in the day, 1100 local time, with a gradual decrease toward nighttime.

DeLiberty, Tracy↗