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Wheeler, Mark M.

Publications and source records attributed to Wheeler, Mark M..

At least 19 records

Assessing Upper-Level Winds on Day-of-Launch

On the day-or-launch. the 45th Weather Squadron Launch Weather Officers (LWOS) monitor the upper-level winds for their launch customers to include NASA's Launch Services Program (LSP). During launch operations, the payload launch team sometimes asks the LWO if they expect the upper level winds to change during the countdown but the LWOs did not have the capability to quickly retrieve or display the upper-level observations and compare them to the numerical weather prediction model point forecasts. The LWOs requested the Applied Meteorology Unit (AMU) develop a capability in the form of a graphical user interface (GUI) that would allow them to plot upper-level wind speed and direction observations from the Kennedy Space Center Doppler Radar Wind Profilers and Cape Canaveral Air Force Station rawinsondes and then overlay model point forecast profiles on the observation profiles to assess the performance of these models and graphically display them to the launch team. The AMU developed an Excel-based capability for the LWOs to assess the model forecast upper-level winds and compare them to observations. They did so by creating a GUI in Excel that allows the LWOs to first initialize the models by comparing the O-hour model forecasts to the observations and then to display model forecasts in 3-hour intervals from the current time through 12 hours.

Bauman, William H., III

Vandenberg Air Force Base Upper Level Wind Launch Weather Constraints

The 30th Operational Support Squadron Weather Flight (30 OSSWF) provides comprehensive weather services to the space program at Vandenberg Air Force Base (VAFB) in California. One of their responsibilities is to monitor upper-level winds to ensure safe launch operations of the Minuteman III ballistic missile. The 30 OSSWF tasked the Applied Meteorology Unit (AMU) to analyze VAFB sounding data with the goal of determining the probability of violating (PoV) their upper-level thresholds for wind speed and shear constraints specific to this launch vehicle, and to develop a tool that will calculate the PoV of each constraint on the day of launch. In order to calculate the probability of exceeding each constraint, the AMU collected and analyzed historical data from VAFB. The historical sounding data were retrieved from the National Oceanic and Atmospheric Administration Earth System Research Laboratory archive for the years 1994-2011 and then stratified into four sub-seasons: January-March, April-June, July-September, and October-December. The maximum wind speed and 1000-ft shear values for each sounding in each subseason were determined. To accurately calculate the PoV, the AMU determined the theoretical distributions that best fit the maximum wind speed and maximum shear datasets. Ultimately it was discovered that the maximum wind speeds follow a Gaussian distribution while the maximum shear values follow a lognormal distribution. These results were applied when calculating the averages and standard deviations needed for the historical and real-time PoV calculations. In addition to the requirements outlined in the original task plan, the AMU also included forecast sounding data from the Rapid Refresh model. This information provides further insight for the launch weather officers (LWOs) when determining if a wind constraint violation will occur over the next few hours on day of launch. The interactive graphical user interface (GUI) for this project was developed in Microsoft Excel using Visual Basic for Applications. The GUI displays the critical sounding data easily and quickly for the LWOs on day of launch. This tool will replace the existing one used by the 30 OSSWF, assist the LWOs in determining the probability of exceeding specific wind threshold values, and help to improve the overall upper winds forecast for the launch customer.

Shafer, Jaclyn A.

Upgrade Summer Severe Weather Tool in MIDDS

The goal of this task was to upgrade the severe weather database from the previous phase by adding weather observations from the years 2004 - 2009, re-analyze the data to determine the important parameters, make adjustments to the index weights depending on the analysis results, and update the MIDDS GUI. The added data increased the period of record from 15 to 21 years. Data sources included local forecast rules, archived sounding data, surface and upper air maps, and two severe weather event databases covering east-central Florida. Four of the stability indices showed increased severe weather predication. The Total Threat Score (TTS) of the previous work was verified for the warm season of 2009 with very good skill. The TTS Probability of Detection (POD) was 88% and the False alarm rate (FAR) of 8%. Based on the results of the analyses, the MIDDS Severe Weather Worksheet GUI was updated to assist the duty forecaster by providing a level of objective guidance based on the analysis of the stability parameters and synoptic-scale dynamics.

Wheeler, Mark M.

Severe Weather and Weak Waterspout Checklist in MIDDS

The goal of this task was to migrate the functionality of the AMU web-based Severe Weather Forecast Decision Aid and the 45 WS Weak Waterspout Checklist to MIDDS, the operational data ingest and display system of the 45 WS. Forecasting the occurrence and timing of warm season severe weather and weak waterspouts is challenging for 45 WS operational personnel. These interactive tools assist forecasters in determining the probability of issuing severe weather watches and warnings for the day. MIDDS is able retrieve many of the needed parameter values for the worksheet automatically. The AMU was able to develop user-friendly tools in MIDDS for both of these tools using McBASI coded programs. The tools retrieve needed values from MIDDS automatically, and require the forecaster to answer a few subjective questions. Both tools were tested and previewed to the 45 WS on MIDDS. In their previous forms, the forecasters enter values into both tools manually to output a threat index. Making these tools more automatic will reduce the possibility of human error and increase efficiency.

Wheeler, Mark M.

Analysis of Rapidly Developing Low Cloud Ceilings in a Stable Environment

Forecasters at the Space Meteorology Group (SMG) issue 30 to 90 minute forecasts for low cloud ceilings at the Space Shuttle Landing Facility (TTS) to support Space Shuttle landings. Mission verification statistics have shown ceilings to be the number one forecast challenge for SMG. More specifically, forecasters at SMG are concerned with any rapidly developing clouds/ceilings below 8000 ft in a stable, capped thermodynamic environment. Therefore, the Applied Meteorology Unit (AMU) was tasked to examine archived events of rapid stable cloud formation resulting in ceilings below 8000 ft, and document the atmospheric regimes favoring this type of cloud development. The AMU examined the cool season months of November to March during the years of 1993-2003 for days that had low-level inversions and rapid, stable low cloud formation that resulted in ceilings violating the Space Shuttle Flight Rules. The AMU wrote and modified existing code to identify inversions from the morning (-10 UTC) Cape Canaveral, FL rawinsonde (XMR) during the cool season and output pertinent sounding information. They parsed all days with cloud ceilings below 8000 ft at TTS, forming a database of possible rapidly-developing low ceiling events. Days with precipitation or noticeable fog burn-off situations were excluded from the database. In the first phase of this work, only the daytime hours were examined for possible ceiling development events since low clouds are easier to diagnose with visible satellite imagery. Phase II of this work includes expanding the database to include nighttime cases which is underway as this abstract is being written. For the nighttime cases, the AMU will analyze both the 00 UTC soundings and the 10 UTC soundings to examine those data for the presence of a low-level inversion. The 00 UTC soundings will probably not have a surface-based inversion, but the presence of inversions or "neutral" layers aloft and below 8,000 ft will most likely help define the stable regime, being a thermodynamically "capped" environment. Occurrences of elevated low-level inversions or stable layers will be highlighted in conjunction with nights that experienced a possible development or onset of cloud ceilings below 8,000 ft. Using these criteria to narrow down the database, the AMU will then use archived IR satellite imagery for these possible events. This presentation summarizes the composite meteorological conditions for 20 daytime event days with rapid low cloud ceiling formation and 48 non-events days consisting of advection or widespread low cloud ceilings and describes two sample cases of daytime rapidly-developing low cloud ceilings. The authors will also summarize the work from the nighttime cases and describe a representative sample case from this data set.

Bauman, William H., III

RSA/Legacy Wind Sensor Comparison: Eastern Range - Part 2

This report describes a comparison of data from ultrasonic and propeller-and-vane anemometers on 5 wind towers at Kennedy Space Center and Cape Canaveral Air Force Station. The ultrasonic sensors are scheduled to replace the Legacy propeller-and-vane sensors under the Range Standardization and Automation (RSA) program. Because previous studies have noted differences between peak wind speeds reported by mechanical and ultrasonic wind sensors, the latter having no moving parts, the 30th and 45th Weather Squadrons wanted to understand possible differences between the two sensor types. The period-of-record was 13-30 May 2005, A total of 357,626 readings of 1-minute average and peak wind speed/direction from each sensor type were used. Statistics of differences in speed and direction were used to identify 15 out of 19 RSA sensors having the most consistent performance, with respect to the Legacy sensors. RSA average wind speed data from these 15 showed a small positive bias of 0.38 kts. A slightly larger positive bias of 0.94 kts was found in the RSA peak wind speed.

Short, David A.

RSA/Legacy Wind Sensor Comparison: Western Range - Part 1

This report describes a comparison of data from ultrasonic and cup-and-vane anemometers on 5 wind towers at Vandenberg AFB. The ultrasonic sensors are scheduled to replace the Legacy cup-and-vane sensors under the Range Standardization and Automation (RSA) program. Because previous studies have noted differences between peak wind speeds reported by mechanical and ultrasonic wind sensors, the latter having no moving parts, the 30th and 45th Weather Squadrons wanted to understand possible differences between the two sensor types. The period-of-record was 13-30 May 2005. A total of 153,961 readings of I-minute average and peak wind speed/direction from each sensor type were used. Statistics of differences in speed and direction were used to identify 18 out of 34 RSA sensors having the most consistent performance, with respect to the Legacy sensors. Data from these 18 were used to form a composite comparison. A small positive bias in the composite RSA average wind speed increased from +0.5 kts at 15 kts, to +1 kt at 25 kts. A slightly larger positive bias in the RSA peak wind speed increased from +1 kt at 15 kts, to +2 kts at 30 kts.

Short, David A.

A Study of Rapidly Developing Low Cloud Ceilings in a Stable Atmosphere at the Florida Spaceport

Forecasters at the Space Meteorology Group (SMG) issue 30 to 90 minute forecasts for low cloud ceilings at the Shuttle Landing Facility (KTTS) in Kennedy Space Center, FL for all Space Shuttle missions. Mission verification statistics have shown cloud ceilings to be the biggest forecast challenge. SMG forecasters are especially concerned with rapidly developing cloud ceilings below 8000 ft. in a stable, capped thermodynamic environment because ceilings below 8000 ft restrict Shuttle landing operations and are the most challenging to predict accurately. This project involves the development of a database of these cases over east-central Florida in order to identify the onset, location, and if possible, dissipation times of rapidly-developing low cloud ceilings. Another goal is to document the atmospheric regimes favoring this type of cloud development to improve forecast skill of such events during Space Shuttle launch and landing operations. A 10-year database of stable, rapid low cloud development days during the daylight hours was compiled for the Florida cool-season months by examining the Cape Canaveral Air Force Station sounding data, and identifying days that had high boundary layer relative humidity associated with a thermally-capped environment below 8000 ft. Archived hourly surface observations from KTTS and Melbourne, Orlando, Sanford, and Ocala, FL were then examined for the onset of cloud ceilings below 8000 ft between 1100 and 2000 UTC. Once the database was supplemented with the hourly surface cloud observations, visible satellite imagery was examined in 30-minute intervals to confirm event occurrences. This paper will present results from some of the rapidly developing cloud ceiling cases and the prevailing meteorological conditions associated with these events, focusing on potential pre-curser information that may help improve their prediction.

FROM

Severe Weather Forecast Decision Aid

This report presents a 15-year climatological study of severe weather events and related severe weather atmospheric parameters. Data sources included local forecast rules, archived sounding data, Cloud-to-Ground Lightning Surveillance System (CGLSS) data, surface and upper air maps, and two severe weather event databases covering east-central Florida. The local forecast rules were used to set threat assessment thresholds for stability parameters that were derived from the sounding data. The severe weather events databases were used to identify days with reported severe weather and the CGLSS data was used to differentiate between lightning and non-lightning days. These data sets provided the foundation for analyzing the stability parameters and synoptic patterns that were used to develop an objective tool to aid in forecasting severe weather events. The period of record for the analysis was May - September, 1989 - 2003. The results indicate that there are certain synoptic patterns more prevalent on days with severe weather and some of the stability parameters are better predictors of severe weather days based on locally tuned threat values. The results also revealed the stability parameters that did not display any skill related to severe weather days. An interactive web-based Severe Weather Decision Aid was developed to assist the duty forecaster by providing a level of objective guidance based on the analysis of the stability parameters, CGLSS data, and synoptic-scale dynamics. The tool will be tested and evaluated during the 2005 warm season.

Bauman, William H., III

Analysis of Rapidly Developing Low Cloud Ceilings in a Stable Environment

This report describes the work done by the Applied Meteorology Unit (AMU) in developing a database of days that experienced rapid (< 90 minutes) low cloud formation in a stable atmosphere, resulting in ceilings at the Shuttle Landing Facility (TTS) that violated Space Shuttle Flight Rules (FR). The meteorological conditions favoring the rapid formation of low ceilings include the presence of any inversion below 8000 ft, high relative humidity beneath the inversion, and a clockwise turning of the winds from the surface to the middle troposphere (approx. 15000 ft). The AMU compared and contrasted the atmospheric and thermodynamic conditions between days with rapid low ceiling formation and days with low ceiling resulting from other mechanism. The AMU found that the vertical wind profile is the probable discerning factor between the rapidly-forming ceiling days and other low ceiling days at TTS. Most rapidly-developing low ceiling days had a clockwise turning of the winds with height, whereas other low ceiling days typically had a counter-clockwise turning of the winds with height or negligible vertical wind shear. Forecasters at the Space Meteorology Group (SMG) issue 30 to 90 minute forecasts for low cloud ceilings at TTS to support Space Shuttle landings. Mission verification statistics have shown ceilings to be the number one forecast challenge. More specifically, forecasters at SMG are concerned with any rapidly developing clouds ceilings below 8000 ft in a stable, capped thermodynamic environment, Therefore, the AMU was tasked to examine archived events of rapid stable cloud formation resulting in ceilings below 8000 ft, and document the atmospheric regimes favoring this type of cloud development. The AMU examined the cool season months of November to March during the years of 1993-2003 for days that had low-level inversions and rapid, stable low cloud formation that resulted in ceilings violating the Space Shuttle FR. The AMU wrote and modified existing code to identify inversions from the morning Cape Canaveral, FL rawinsonde (XMR) during the cool season and output pertinent sounding information. They parsed all days with cloud ceilings below 8000 ft at TTS, forming a database of possible rapidly-developing low ceiling events. Days with precipitation or noticeable fog bum-off situations were excluded from the database. Only the daytime hours were examined for possible ceiling development events since low clouds are easier to diagnose with visible satellite imagery. Follow-on work would expand the database to include nighttime cases, using a special enhancement of the infrared imagery for identifying areas of low clouds. The report presents two sample cases of rapidly-developing low cloud ceilings. These cases depict the representative meteorological and thermodynamic characteristics of such events. The cases also illustrate how quickly the cloud decks can develop, sometimes forming in 30 minutes or less. The report also summarizes the composite meteorological conditions for 20 event days with rapid low cloud ceiling formation and 48 non-events days consisting of advection or widespread low cloud ceilings. The meteorological conditions were quite similar for both the event and non-event days, since both types of days experienced low cloud ceilings. Both types of days had a relatively moist environment beneath the inversion based below 8000 ft. In the 20 events identified, de onset of low ceilings occurred between 1200-1800 UTC in every instance. The distinguishing factor between the event and non-event days appears to be the vertical wind profile in the XMR sounding. Eighty-five percent of the event days had a clockwise turning of the winds with height in the lower to middle troposphere whereas 83% of the non-events had a counter-clockwise turning of the winds with height or negligible vertical wind shear. A clockwise turning of the winds with height indicates a warm advection regime, which supports large-scale rising motn and possible cloud formation. Meanwhile, a counter-clockwise turning of the winds with height indicates cold advection or sinking motion in a post-cold frontal environment.

Wheeler, Mark M.

Remotely actuated localized pressure and heat apparatus and method of use

Apparatus and method for the use of a remotely actuated localized pressure and heat apparatus for the consolidation and curing of fiber elements in, structures. The apparatus includes members for clamping the desired portion of the fiber elements to be joined, pressure members and/or heat members. The method is directed to the application and use of the apparatus.

Merret, John B.

Nowcasting Thunderstorm Anvil Clouds Over KSC/CCAFS

Electrified thunderstorm anvil clouds extend the threat of natural and triggered lightning to space launch and landing operations far beyond the immediate vicinity of thunderstorm cells. The deep convective updrafts of thunderstorms transport large amounts of water vapor, super-cooled water droplets and ice crystals into the upper troposphere, forming anvil clouds, which are then carried downstream by the prevailing winds in the anvil formation layer. Electrified anvil clouds have been observed over the space launch and landing facilities of Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS), emanating from thunderstorm activity more than 200 km distant. Space launch commit criteria and flight rules require launch and landing vehicles to avoid penetration of the non-transparent portion of anvil clouds. The life cycles of 167 anvil clouds over the Florida peninsula and its coastal waters were documented using GOES-8 visible imagery on 50 anvil case days during the months of May through July 2001. Anvil clouds were found to propagate at the speed and direction of upper-tropospheric winds in the layer from 300-to-l50 mb, approximately 9.4 km to 14 km, with an effective average transport lifetime of 2 hours and a standard deviation of approximately 30 minutes. The effective lifetime refers to the time required for the nontransparent leading edge of an anvil cloud to reach its maximum extent before beginning to dissipate. The propagation and lifetime information was incorporated into the design, construction and implementation of an objective short-range anvil forecast tool based on upper-air observations, for use on the Meteorological Interactive Data Display System within the Range Weather Operations facility of the 45th Weather Squadron at CCAFS and the Spaceflight Meteorology Group at Johnson Space Center.

Short, David A.

MiniSODAR(TradeMark) Evaluation

This report describes results of the AMU's Instrumentation and Measurement task for evaluation of the Doppler miniSODAR(TradeMark) System (DmSS). The DmSS is an acoustic wind profiler providing high resolution data to a height of approx. 410 ft. The Boeing Company installed a DmSS near Space Launch Complex 37 in mid-2002 as a substitute for a tall wind tower and plans to use DmSS data for the analysis and forecasting of winds during ground and launch operations. Peak wind speed data are of particular importance to Launch Weather Officers of the 45th Weather Squadron for evaluating user Launch Commit Criteria. The AMU performed a comparative analysis of wind data between the DmSS and nearby wind towers from August 2002 to July 2003. The DmSS vertical profile of average wind speed showed good agreement with the wind towers. However, the DMSS peak wind speeds were higher, on average, than the wind tower peak wind speeds by about 25%. A statistical model of an idealized Doppler profiler was developed and it predicted that average wind speeds would be well determined but peak wind speeds would be over-estimated due to an under-specification of vertical velocity variations in the atmosphere over the Profiler.

Short, David A.

Land-Breeze Forecasting

The nocturnal land breeze at the Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) is both operationally significant and challenging to forecast. The occurrence and timing of land breezes impact low-level winds, atmospheric stability, low temperatures, and fog development. Accurate predictions of the land breeze are critical for toxic material dispersion forecasts associated with space launch missions, since wind direction and low-level stability can change noticeably with the onset of a land breeze. This report presents a seven-year observational study of land breezes over east-central Florida from 1995 to 2001. This comprehensive analysis was enabled by the high-resolution tower observations over KSC/CCAFS. Five-minute observations of winds, temperature, and moisture along with 9 15-MHz Doppler Radar Wind Profiler data were used to analyze specific land-breeze cases, while the tower data were used to construct a composite climatology. Utilities derived from this climatology were developed to assist forecasters in determining the land-breeze occurrence, timing, and movement based on predicted meteorological conditions.

Case, Jonathan L.

WSR-88D Cell Trends

This report documents the Applied Meteorology Unit's evaluation of the Cell Trends display as a tool for radar operators to use in their evaluation of storm cell strength. The objective of the evaluation is to assess the utility of the WSR-88D graphical Cell Trends display for local radar cell interpretation in support of the 45th Weather Squadron (45 WS), Spaceflight Meteorology Group (SMG), and National Weather Service (NWS) Melbourne (MLB) operational requirements. The analysis procedure was to identify each cell and track the maximum reflectivity, height of maximum reflectivity, storm top, storm base, hail and severe hail probability, cell-based Vertically Integrated Liquid (VIL) and core aspect ratio using WATADS Build 9.0 cell trends information. One problem noted in the analysis phase was that the Storm Cell Identification and Tracking (SCIT) algorithm had a difficult time tracking the small cells associated with the Florida weather regimes. The analysis indicated numerous occasions when a cell track would end or an existing cell would be give a new ID in the middle of its life cycle. This investigation has found that most cells, which produce hail or microburst events, have discernable Cell Trends signatures. Forecasters should monitor the PUP's Cell Trends display for cells that show rapid (1 scan) changes in both the heights of maximum reflectivity and cell-based VIEL. It is important to note that this a very limited data set (four case days). Fifty-two storm cells were analyzed during those four days. The above mentioned t=ds, increase in the two cell attributes for hail events and decrease in the two cell attributes for wind events were noted in most of the cells. The probability of detection was 88% for both events. The False Alarm Rate (FAR) was a 36% for hail events and a respectable 25% for microburst events. In addition the Heidke Skill Score (HSS) is 0.65 for hail events and 0.67 for microburst events. For random forecast the HSS is 0 and that a perfect score is 1.

Wheeler, Mark M.

Report on the Radar/PIREP Cloud Top Discrepancy Study

This report documents the results of the Applied Meteorology Unit's (AMU) investigation of inconsistencies between pilot reported cloud top heights and weather radar indicated echo top heights (assumed to be cloud tops) as identified by the 45 Weather Squadron (45WS). The objective for this study is to document and understand the differences in echo top characteristics as displayed on both the WSR-88D and WSR-74C radars and cloud top heights reported by the contract weather aircraft in support of space launch operations at Cape Canaveral Air Station (CCAS), Florida. These inconsistencies are of operational concern since various Launch Commit Criteria (LCC) and Flight Rules (FR) in part describe safe and unsafe conditions as a function of cloud thickness. Some background radar information was presented. Scan strategies for the WSR-74C and WSR-88D were reviewed along with a description of normal radar beam propagation influenced by the Effective Earth Radius Model. Atmospheric conditions prior to and leading up to both launch operations were detailed. Through the analysis of rawinsonde and radar data, atmospheric refraction or bending of the radar beam was identified as the cause of the discrepancies between reported cloud top heights by the contract weather aircraft and those as identified by both radars. The atmospheric refraction caused the radar beam to be further bent toward the Earth than normal. This radar beam bending causes the radar target to be displayed erroneously, with higher cloud top heights and a very blocky or skewed appearance.

Wheeler, Mark M.

AMU NEXRAD Exploitation Task

This report documents the results of the Applied Meteorology Unit's NEXRAD Exploitation Task. The objectives of this task are to determine what radar signatures are present prior to and at the time of convection initiation, and to determine radar signatures which will help distinguish whether the ensuing convection will become severe. Radar data from the WSR-88D radar located at NWS Melbourne (WSR-88D/KMLB) were collected between June and September 1995, and 16 convective case studies were analyzed for which the radar was operating during the entire period of interest. All WSR-88D/KMLB products were scrutinized for their utility in detecting convection initiation and severe storm signatures. Through process of elimination, it was found that the 0.5 deg reflectivity product with the lowest reflectivity values displayed is the best product to monitor for convection initiation signatures. Seven meteorological features associated with the initiation of deep convection were identified: the Merritt Island and Indian River convergence zones, interlake convergence, horizontal convective rolls, the sea breeze, storm outflow boundaries, and fires. Their reflectivity values ranged from -5 to 20 dBZ. Of the three severe weather phenomena (winds greater than or equal to 50 kts, tornado, 3/4 inch hail), high wind events due to microbursts were most common in the data set. It was found that the values and trends of composite reflectivity, vertically integrated liquid, and core aspect ratio were key indicators of the potential of a cell to produce a microburst. The data were not analyzed for the other two severe weather phenomena because they rarely occurred during the data collection period. This report also includes suggestions for new WSR-88D products, summaries of ongoing research aimed at creating new products, and explicit recommended procedures for detecting convection initiation and severe storm signatures in the radar data using the currently available technology.

Lambert, Winifred C.

Evaluation of the Emergency Response Dose Assessment System(ERDAS)

The emergency response dose assessment system (ERDAS) is a protype software and hardware system configured to produce routine mesoscale meteorological forecasts and enhanced dispersion estimates on an operational basis for the Kennedy Space Center (KSC)/Cape Canaveral Air Station (CCAS) region. ERDAS provides emergency response guidance to operations at KSC/CCAS in the case of an accidental hazardous material release or an aborted vehicle launch. This report describes the evaluation of ERDAS including: evaluation of sea breeze predictions, comparison of launch plume location and concentration predictions, case study of a toxic release, evaluation of model sensitivity to varying input parameters, evaluation of the user interface, assessment of ERDA's operational capabilities, and a comparison of ERDAS models to the ocean breeze dry gultch diffusion model.

Evans, Randolph J.