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NASA NTRS1997

Scale Model Icing Research Tunnel

NASA Lewis Research Center's Icing Research Tunnel (IRT) is the world's largest refrigerated wind tunnel and one of only three icing wind tunnel facilities in the United States. The IRT was constructed in the 1940's and has been operated continually since it was built. In this facility, natural icing conditions are duplicated to test the effects of inflight icing on actual aircraft components as well as on models of airplanes and helicopters. IRT tests have been used successfully to reduce flight test hours for the certification of ice-detection instrumentation and ice protection systems. To ensure that the IRT will remain the world's premier icing facility well into the next century, Lewis is making some renovations and is planning others. These improvements include modernizing the control room, replacing the fan blades with new ones to increase the test section maximum velocity to 430 mph, installing new spray bars to increase the size and uniformity of the artificial icing cloud, and replacing the facility heat exchanger. Most of the improvements will have a first-order effect on the IRT's airflow quality. To help us understand these effects and evaluate potential improvements to the flow characteristics of the IRT, we built a modular 1/10th-scale aerodynamic model of the facility. This closed-loop scale-model pilot tunnel was fabricated onsite in the various shops of Lewis' Fabrication Support Division. The tunnel's rectangular sections are composed of acrylic walls supported by an aluminum angle framework. Its turning vanes are made of tubing machined to the contour of the IRT turning vanes. The fan leg of the tunnel, which transitions from rectangular to circular and back to rectangular cross sections, is fabricated of fiberglass sections. The contraction section of the tunnel is constructed from sheet aluminum. A 12-bladed aluminum fan is coupled to a turbine powered by high-pressure air capable of driving the maximum test section velocity to 550 ft/sec (Mach 0.45). The air turbine and instrumentation are housed inside a fiberglass nacelle. Total and static pressure measurements can be taken around the loop, and velocity and flow angularity measurements can be taken with hot-wire and five-hole probes at specific locations. The Scale Model Icing Research Tunnel (SMIRT) is undergoing checkout tests to determine how its airflow characteristics compare with the IRT. Near-term uses for this scale-model tunnel include determining the aerodynamic effects of replacing the 52-yearold W-shaped heat exchanger with a flat-faced heat exchanger. SMIRT is an integral part of the improvements planned for the IRT because testing the proposed IRT improvements in a scale-model tunnel will lower costs and improve productivity.

Canacci, Victor A.↗

NASA NTRS2005

"Cosmological Parameters from Large Scale Structure"

This grant has provided primary support for graduate student Mark Neyrinck, and some support for the PI and for colleague Nick Gnedin, who helped co-supervise Neyrinck. This award had two major goals. First, to continue to develop and apply methods for measuring galaxy power spectra on large, linear scales, with a view to constraining cosmological parameters. And second, to begin try to understand galaxy clustering at smaller. nonlinear scales well enough to constrain cosmology from those scales also. Under this grant, the PI and collaborators, notably Max Tegmark. continued to improve their technology for measuring power spectra from galaxy surveys at large, linear scales. and to apply the technology to surveys as the data become available. We believe that our methods are best in the world. These measurements become the foundation from which we and other groups measure cosmological parameters.

Hamilton, A. J. S.↗

NASA NTRS2005

A Coupled fcGCM-GCE Modeling System: A 3D Cloud Resolving Model and a Regional Scale Model

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and ore sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (21CE, several 31CE), Goddard radiation (including explicity calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generation regional scale model, WRF. In this talk, I will present: (1) A Brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), (3) A discussion on the Goddard WRF version (its developments and applications), and (4) The characteristics of the four-dimensional cloud data sets (or cloud library) stored at Goddard.

Tao, Wei-Kuo↗

NASA NTRS2006

Latest Developments in SLD Scaling

Scaling methods have been shown previously to work well for super cooled large droplet (SLD) main ice shapes. However, feather sizes for some conditions have not been well represented by scale tests. To determine if there are fundamental differences between the development of feathers for appendix C and SLD conditions, this study used time-sequenced photographs, viewing along the span of the model during icing sprays. An airspeed of 100 kt, cloud water drop MVDs of 30 and 140 microns, and stagnation freezing fractions of 0.30 and 0.50 were tested in the NASA Glenn Icing Research Tunnel using an unswept 91-cm-chord NACA0012 airfoil model mounted at 0deg AOA. The photos indicated that the feathers that developed in a distinct region downstream of the leading-edge ice determined the horn location and angle. The angle at which feathers grew from the surface were also measured; results are shown for an airspeed of 150 kt, an MVD of 30 microns, and stagnation freezing fractions of 0.30 to 0.60. Feather angles were found to depend strongly on the stagnation freezing fraction, and were independent of either chordwise position on the model or time into the spray. Feather angles also correlated well with horn angles. For these tests, there did not appear to be fundamental differences between the physics of SLD and appendix C icing; therefore, for these conditions similarity parameters used for appendix C scaling appear to be valid for SLD scaling as well. Further investigation into the cause for the large feather structures observed for some SLD conditions will continue.

Tsao, Jen-Ching↗

NASA NTRS2006

A Coupled GCM-Cloud Resolving Modeling System, and A Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (21CE, several 31CE), Goddard radiation (including explicitly calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generation regional scale model, WRF. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗

NASA NTRS2006

The TRMM Multi-satellite Precipitation Analysis (TMPA): Quasi-Global Precipitation Estimates at Fine Scales

The TRMM Multi-satellite Precipitation Analysis (TMPA) provides a calibration-based sequential scheme for combining multiple precipitation estimates from satellites, as well as gauge analyses where feasible, at fine scales (0.25 degrees x 0.25 degrees and 3-hourly). It is available both after and in real time, based on calibration by the TRMM Combined Instrument and TRMM Microwave Imager precipitation products, respectively. Only the after-real-time product incorporates gauge data at the present. The data set covers the latitude band 50 degrees N-S for the period 1998 to the delayed present. Early validation results are as follows: The TMPA provides reasonable performance at monthly scales, although it is shown to have precipitation rate dependent low bias due to lack of sensitivity to low precipitation rates in one of the input products (based on AMSU-B). At finer scales the TMPA is successful at approximately reproducing the surface-observation-based histogram of precipitation, as well as reasonably detecting large daily events. The TMPA, however, has lower skill in correctly specifying moderate and light event amounts on short time intervals, in common with other fine-scale estimators. Examples are provided of a flood event and diurnal cycle determination.

Huffman, George J.↗

NASA NTRS2006

Ultra-fine-scale filamentary structures in the Outer Corona and the Solar Magnetic Field

Filamentary structures following magnetic field lines pervade the Sun's atmosphere and offer us insight into the solar magnetic field. Radio propagation measurements have shown that the smallest filamentary structures in the solar corona are more than 2 orders of magnitude finer than those seen in solar imaging. Here we use radio Doppler measurements to characterize their transverse density gradient and determine their finest scale in the outer corona at 20-30 R(circled dot operator), where open magnetic fields prevail. Filamentary structures overly active regions have the steepest gradient and finest scale, while those overlying coronal holes have the shallowest gradient and least finest scale. Their organization by the underlying corona implies that these subresolution structures extend radially from the entire Sun, confirming that they trace the coronal magnetic field responsible for the radial expansion of the solar wind. That they are rooted all over the Sun elucidates the association between the magnetic field of the photosphere and that of the corona, as revealed by the similarity between the power spectra of the photospheric field and the coronal density fluctuations. This association along with the persistence of filamentary structures far from the Sun demonstrate that subresolution magnetic fields must play an important role not only in magnetic coupling of the photosphere and corona, but also in coronal heating and solar wind acceleration through the process of small-scale magnetic reconnection. They also explain why current widely used theoretical models that extrapolate photospheric magnetic fields into the corona do not predict the correct source of the solar wind.

Sun : Corona↗

NASA NTRS2004

Aeroacoustic Study of a 26%-Scale Semispan Model of a Boeing 777 Wing in the NASA Ames 40- by 80-Foot Wind Tunnel

An acoustic and aerodynamic study was made of a 26%-scale unpowered Boeing 777 aircraft semispan model in the NASA Ames 40- by 80-Foot Wind Tunnel for the purpose of identifying and attenuating airframe noise sources. Simulated approach and landing configurations were evaluated at Mach numbers between 0.12 and 0.24. Cruise configurations were evaluated at Mach numbers between 0.24 and 0.33. The research team used two Ames phased-microphone arrays, a large fixed array and a small traversing array, mounted under the wing to locate and compare various noise sources in the wing high-lift system and landing gear. Numerous model modifications and noise alleviation devices were evaluated. Simultaneous with acoustic measurements, aerodynamic forces were recorded to document aircraft conditions and any performance changes caused by the geometric modifications. Numerous airframe noise sources were identified that might be important factors in the approach and landing noise of the full-scale aircraft. Several noise-control devices were applied to each noise source. The devices were chosen to manipulate and control, if possible, the flow around the various tips and through the various gaps of the high-lift system so as to minimize the noise generation. Fences, fairings, tip extensions, cove fillers, vortex generators, hole coverings, and boundary-layer trips were tested. In many cases, the noise-control devices eliminated noise from some sources at specific frequencies. When scaled to full-scale third-octave bands, typical noise reductions ranged from 1 to 10 dB without significant aerodynamic performance loss.

Horne, W. Clifton↗

NASA NTRS2007

A Coupled GCM-Cloud Resolving Modeling System, and a Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a superparameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (2ICE, several 31CE), Goddard radiation (including explicitly calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generatio11 regional scale model, WRF. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗

NASA NTRS2007

Nonlinear Structural Analysis Methodology and Dynamics Scaling of Inflatable Parabolic Reflector Antenna Concepts

Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are presented to show how surface wrinkle progress with increasing tension loads. Antenna reflector surface accuracies were found to be very much dependent on the type and size of the antenna, the reflector surface curvature, reflector membrane supports in terms of spacing of catenaries, as well as the amount of applied load.

Sreekantamurthy, Tham↗

NASA NTRS1963

Aeroelastic Tests of an Eight Percent Scale Saturn C-1 Block II

Buffet and flutter characteristics of Saturn Apollo mission were studied using a dynamically scaled model. The model was built around a central aluminum tube for scaled stiffness distribution and strength to resist loads imposed during testing. Styrofoam sections attached to the core provided the correct external contours. Lead weights were added for correct mass distribution. An electromagnetic shaker was used to excite the model in its flexible modes of vibration during portions of the test. The model was supported on a sting, mounted by leaf springs, cables and torsion bars. The support system provided for simulating the full scale rigid body pitch frequency with minimum restraint imposed on elastic deflections. Bending moments recorded by sensors on the aluminum tube. Several modified nose configurations were tested: The basic configuration was tested with and without a flow separator disk on the escape rocket motor, tests also were made with the escape tower and rocket motor removed completely. For the final test, the Apollo capsule was replaced with a Jupiter nose cone. The test program consisted of determining model response throughout the transonic speed range at angles of attack up to 6 degrees and measuring the aerodynamic damping over the same range for the basic model and the modified configurations. Signals from the model pickup were recorded on tape for later analysis. The data obtained were used to estimate bending moments that would be produced on the full-scale vehicle by aerodynamic forces due to buffeting.

EXPERIMENTS↗

NASA NTRS2004

Single Event Effects in Highly Scaled Devices for Space Applications

This paper discusses single-event upset (SEU) in memories and microprocessors that are the "drivers" of highly scaled commercial integrated circuits. Despite the decrease in critical charge that occurs for highly scaled CMOS devices, recent test data has shown that SEU rates are actually somewhat lower for scaled devices compared to older devices with larger feature size. Hard errors, which are increasingly important for memories, are discussed along with conventional soft errors. Functional errors in memories and microprocessors are particularly significant, and tend to dominate the response of highly scaled devices from an application standpoint. Predictions for future devices are made using the Semiconductor Industry Roadmap along with recent modeling and radiation test results.

microelectronics↗

NASA NTRS2007

Scaling of Performance in Liquid Propellant Rocket Engine Combustors

This paper discusses scaling of combustion and combustion performance in liquid propellant rocket engine combustion devices. In development of new combustors, comparisons are often made between predicted performance in a new combustor and measured performance in another combustor with different geometric and thermodynamic characteristics. Without careful interpretation of some key features, the comparison can be misinterpreted and erroneous information used in the design of the new device. This paper provides a review of this performance comparison, including a brief review of the initial liquid rocket scaling research conducted during the 1950s and 1960s, a review of the typical performance losses encountered and how they scale, a description of the typical scaling procedures used in development programs today, and finally a review of several historical development programs to see what insight they can bring to the questions at hand.

Hulka, James R.↗

NASA NTRS2008

Multiscale Modeling of Damage Processes in Aluminum Alloys: Grain-Scale Mechanisms

This paper has two goals related to the development of a physically-grounded methodology for modeling the initial stages of fatigue crack growth in an aluminum alloy. The aluminum alloy, AA 7075-T651, is susceptible to fatigue cracking that nucleates from cracked second phase iron-bearing particles. Thus, the first goal of the paper is to validate an existing framework for the prediction of the conditions under which the particles crack. The observed statistics of particle cracking (defined as incubation for this alloy) must be accurately predicted to simulate the stochastic nature of microstructurally small fatigue crack (MSFC) formation. Also, only by simulating incubation of damage in a statistically accurate manner can subsequent stages of crack growth be accurately predicted. To maintain fidelity and computational efficiency, a filtering procedure was developed to eliminate particles that were unlikely to crack. The particle filter considers the distributions of particle sizes and shapes, grain texture, and the configuration of the surrounding grains. This filter helps substantially reduce the number of particles that need to be included in the microstructural models and forms the basis of the future work on the subsequent stages of MSFC, crack nucleation and microstructurally small crack propagation. A physics-based approach to simulating fracture should ultimately begin at nanometer length scale, in which atomistic simulation is used to predict the fundamental damage mechanisms of MSFC. These mechanisms include dislocation formation and interaction, interstitial void formation, and atomic diffusion. However, atomistic simulations quickly become computationally intractable as the system size increases, especially when directly linking to the already large microstructural models. Therefore, the second goal of this paper is to propose a method that will incorporate atomistic simulation and small-scale experimental characterization into the existing multiscale framework. At the microscale, the nanoscale mechanics are represented within cohesive zones where appropriate, i.e. where the mechanics observed at the nanoscale can be represented as occurring on a plane such as at grain boundaries or slip planes at a crack front. Important advancements that are yet to be made include: 1. an increased fidelity in cohesive zone modeling; 2. a means to understand how atomistic simulation scales with time; 3. a new experimental methodology for generating empirical models for CZMs and emerging materials; and 4. a validation of simulations of the damage processes at the nano-micro scale. With ever-increasing computer power, the long-term ability to employ atomistic simulation for the prognosis of structural components will not be limited by computation power, but by our lack of knowledge in incorporating atomistic models into simulations of MSFC into a multiscale framework.

Hochhalter, J. D.↗

NASA NTRS2008

A Multi-Scale Modeling System with Unified Physics

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 km, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. In recent years, exponentially increasing computer power has extended cloud-resolving-mode1 integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 km2 in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique.

Tao, Wei-Kuo↗

NASA NTRS2008

Scaling of Performance in Liquid Propellant Rocket Engine Combustion Devices

Hulka, James R.↗

NASA NTRS1954

Free-Flight Tests of 0.11-Scale North American F-100 Airplane Wings to Investigate the Possibility of Flutter in Transonic Speed Range at Varying Angles of Attack

Free-flight tests in the transonic speed range utilizing rocketpropelled models have been made on three pairs of 0.11-scale North American F-100 airplane wings having an aspect ratio of 3.47, a taper ratio of 0.308, 45 degree sweepback at the quarter-chord line, and thickness ratios of 31 and 5 percent to investigate the possibility of flutte r. Data from tests of two other rocket-propelled models which accidentally fluttered during a drag investigation of the North American F-100 airplane are also presented. The first set of wings (5 percent thick) was tested on a model which was disturbed in pitch by a moving tail and reached a maximum Mach number of 0.85. The wings encountered mild oscillations near the first - bending frequency at high lift coefficients. The second set of wings 9 percent thick was tested up to a maximum Mach number of 0.95 at (2) angles of attack provided by small rocket motors installed in the nose of the model. No oscillations resembling flutter were encountered during the coasting flight between separation from the booster and sustainer firing (Mach numbers from 0.86 to 0.82) or during the sustainer firing at accelerations of about 8g up to the maximum Mach number of the test (0.95). The third set of wings was similar to the first set and was tested up to a maximum Mach number of 1.24. A mild flutter at frequencies near the first-bending frequency of the wings was encountered between a Mach number of 1.15 and a Mach number of 1.06 during both accelerating and coasting flight. The two drag models, which were 0.ll-scale models of the North American F-100 airplane configuration, reached a maximum Mach number of 1.77. The wings of these models had bending and torsional frequencies which were 40 and 89 percent, respectively, of the calculated scaled frequencies of the full-scale 7-percent-thick wing. Both models experienced flutter of the same type as that experienced-by the third set of wings.

O'Kelly, Burke R.↗

NASA NTRS2009

Identifying Optimal Temporal Scale for the Correlation of AOD and Ground Measurements of PM2.5 to Improve the Model Performance in a Real-time Air Quality Estimation System

Aerosol optical depth (AOD), an indirect estimate of particle matter using satellite observations, has shown great promise in improving estimates of PM 2.5 air quality surface. Currently, few studies have been conducted to explore the optimal way to apply AOD data to improve the model accuracy of PM 2.5 surface estimation in a real-time air quality system. We believe that two major aspects may be worthy of consideration in that area: 1) the approach to integrate satellite measurements with ground measurements in the pollution estimation, and 2) identification of an optimal temporal scale to calculate the correlation of AOD and ground measurements. This paper is focused on the second aspect on the identifying the optimal temporal scale to correlate AOD with PM2.5. Five following different temporal scales were chosen to evaluate their impact on the model performance: 1) within the last 3 days, 2) within the last 10 days, 3) within the last 30 days, 4) within the last 90 days, and 5) the time period with the highest correlation in a year. The model performance is evaluated for its accuracy, bias, and errors based on the following selected statistics: the Mean Bias, the Normalized Mean Bias, the Root Mean Square Error, Normalized Mean Error, and the Index of Agreement. This research shows that the model with the temporal scale of within the last 30 days displays the best model performance in this study area using 2004 and 2005 data sets.

Li, Hui↗