GIS-based Radar Rainfall Verification. Braxton Edwards

Transcription

1 GIS-based Radar Rainfall Verification Braxton Edwards Academic Affiliation, Fall 2006: Senior, University of Oklahoma SOARS Summer 2006 Science Research Mentors: Olga Wilhelmi, David Yates Writing and Communication Mentor: Cindy Worster Hydrological models and flash flood warning systems are largely dependent on accurate precipitation inputs. In the Colorado Front Range estimation of rainfall has been problematic due to the varying intensity and spatial distribution of the precipitation fields. The goal of this project was to conduct a Geographic Information Systems-based spatial analysis and verification of the radar-derived precipitation. Rain gage measurements were used for correcting radar rainfall estimates over a 24-hour period for convective and stratiform precipitation events over the Denver Urban Drainage and Flood Control District. Two methods were tested for correcting radar-derived precipitation: 1) mean difference between recorded gage values and the radar measurements and 2) mean difference of the inverse distance weighted (IDW) interpolated gage values and the radar measurements. An overall comparison of radar and gage measurements for the two rain events showed that the radar produced more spatially accurate precipitation estimates during a convective event. The IDW interpolated precipitation method was found more appropriate for regional scale verification. The methodology developed in this study provides a framework for spatial rainfall verification, which can aid in automated correction of radar rainfall estimates. This can assist flood control and emergency managers in mitigating and responding to flash flood events. The Significant Opportunities in Atmospheric Research and Science (SOARS) Program is managed by the University Corporation for Atmospheric Research (UCAR) with support from participating universities. SOARS is funded by the National Science Foundation, the National Oceanic and Atmospheric Administration (NOAA) Climate Program Office, the NOAA Oceans and Human Health Initiative, and the Cooperative Institute for Research in Environmental Sciences. SOARS also receives funding from the National Center for Atmospheric Research (NCAR) Biogeosciences Initiative and the NCAR Earth Observing Laboratory. SOARS is a partner project with Research Experience in Solid Earth Science for Student (RESESS).

2 Introduction The Colorado Front Range is an important and challenging region for flash flood forecasting and management. This region is known for extreme precipitation events such as the Big Thompson Canyon, Colorado event in July 1976 and the Ft. Collins event in July of Each of these events had an extreme amount of precipitation over a small area. The spatial distribution of rainfall is critical in flood forecasting in terms of warning people at risk. Often severe downpours occur in one location, where as a location downstream of the event may not be receiving any rain at all. This problem is further enhanced with the mountain upslope of the Front Range, where canyons enhance the velocity and intensity of the water flow. A large portion of the Front Range population lives in areas prone to flash flooding and possible extreme precipitation events. Therefore, accurate precipitation estimates that translate into timely flash flood warnings are an important and challenging problem for the Front Range. The study area for this project, the Urban Drainage and Flood Control District (UDFCD), was created in 1969 to aid local governments in the Denver metropolitan area with multijurisdictional drainage and flood control problems. This district covers an area of over 1600 sq miles, including Denver and six surrounding counties, and has around 2.3 million residents [UDFCD, 2006]. For monitoring urban drainage and potential flooding, the UDFCD has installed 175 Automated Local Evaluation in Real Time (ALERT) stations, 152 rain gages, 87 stream gages, and 18 weather stations positioned through out the UDFCD and surrounding tributaries (Figure 1). Each of these stations has sensors which transmit environmental data to the central computer at the UDFCD (Figure 1) in real time. This system provides for real time data acquisition, automated hydrologic/hydraulic modeling, and automated flood warnings for the counties and jurisdictions of the UDFCD (i.e., Adams County Communications, Arapahoe County 911 Emergency Resource Center, Aurora Fire Communications, Broomfield Police Department Communications, Boulder Sheriff's Communications, Denver Office of Emergency Management, Douglas County Sheriff's Department Communications, and Jefferson County Communications). SOARS 2006, Braxton Edwards, 2

3 Figure 1. Urban Drainage and Flood Control District. In order to make quick and timely decisions about the flash flood warnings, the emergency officials must have knowledge of future, current, and past weather conditions of the area. There are many factors that contribute into the flood warning decision process (Figure 2). The UDFCD, for example, relies heavily on precipitation forecast from both the National Weather Service and private meteorology forecasting companies. Precipitation forecast and information received from the ALERT gage network contribute to the precipitation estimate that in turn is used in a hydrological model for flash flood forecasting. SOARS 2006, Braxton Edwards, 3

4 Flood Warning Decision Process NWS Flood Warning Alert Network of Gages HDR Forecast UDFCD Knowledge of Area Precipitation Hydrological Model Figure 2. Flood Warning Decision Process. Precipitation is a key parameter in determining flood probabilities and water budgets. An accurate assessment of precipitation leads to more accurate modeling of hydrological processes and flash flood forecasting. There have been many different methods developed to accomplish this task [Apaydin et al., 2004]. While some methods have had more success than others, the accuracy in determining the amount of precipitation depends on the type of geographic environment. Here we discuss two main methods for precipitation estimation: rain gages and radars. Rain gages One method scientists use to measure rainfall amounts is tipping bucket rain gages (Figure 3). These platforms respond by accumulating rain in.04 inch increments. Each time the bucket reaches the limit of.04 inches it tips, which results in the electronic signal of the tip being sent to the control station. It provides accurate point measurements of precipitation events. However there are disadvantages to the tipping bucket in the fact that wind may deflect precipitation away from the site, blockage due to buildings, plants, electronic signal malfunctions, mechanical problems, and insects/animals. Wind speeds on the order of 39 miles per hour or greater have been associated with a 50% loss in precipitation to the gage. During intense rainfall events, the gages have difficulty keeping pace, which in tern results in a loss of precipitation during the ½ second it takes the bucket to tip. In general rain gages provide good exposure, easy to maintain, but one should expect an error of 20% or more for convective rainfall. So if the storm is estimated to be 10 inches, the gage may be off by 2 inches. SOARS 2006, Braxton Edwards, 4

5 Figure 3. Tipping Bucket Rain Gage (source: Cambridge Bay Weather, 2005) Spatial Interpolation There are many methods for spatial interpolation of data between gages. On rainfall data, spatial interpolation is mainly done using a variety of techniques that range from inverse distance weighting (IDW), completely regularized spline (CRS), regularized spline with tension (RST), kriging, ordinary kriging (KO), universal kriging (KU), and cokriging [Apaydin, et. al. 2004]. Accuracy of the results of these methods depend on the amount of samples one has [Dirks et. al. 1998]. Each of these methods has been based on the principle of using known point values to estimates values at unknown points. There are several ways of classifying spatial interpolation methods. There are global and local interpolation, exact and inexact interpolation, and deterministic and stochastic interpolation. The local interpolation uses a sample of known points in order to estimate an unknown point. The difference between deterministic and stochastic is in the fact that a deterministic interpolation yields no assessment of errors while the stochastic does. Finally the exact interpolation estimates surfaces that pass through known points, while inexact determines values that differ from known values. For interpolating precipitation data, mainly the local and exact types of interpolation methods have been used. Mostly common interpolation methods include kriging, cokriging, inverse distance weighting (IDW), regularized spline, and spline with tension [Chang, 2004], [Franke, 1982], [Naoum and Tsanis, 2004]. Radar Another method for precipitation estimates is radar. The radar creates an electromagnetic energy pulse which is focused by an antenna and transmitted through the atmosphere. Objects in the path of this electromagnetic pulse, such as rain drops, scatter the electromagnetic energy. The energy that is scattered back to the radar is measured in decibels relative to a reflectivity of 1 mm 6 /m 3 (dbz) [Rinehart, 1991]. Radars have the advantage of being able to measure over a larger area often over a 2-km by 2-km (1.5 mi sq area) or better [Curtis D et al. 1999]. A meteorological radar gives an average of the precipitation falling within a given 1.5 mi sq area, but the amount of a precipitation falling within that area at a given spot may be above or below that average. For example, radar typically overestimates the rainfall if strong updrafts hold up precipitation over an area of dry air below. This causes evaporation below the radar beam thus giving a higher precipitation accumulation that what is actually occurring. This situation SOARS 2006, Braxton Edwards, 5

6 typically takes place in regions of storm growth and leading storm edges. The opposite situation occurs in intense downdraft regions, where rainfall underestimation occurs. This is typical in areas of heavy precipitation storm cores and weakening storm cells. The radar data used in this project come from the Weather Surveillance Radar 88 Doppler (WSR-88D), which has been described as the next generation weather radar. The WSR-88D is the first system to combine advanced radar design, data processing, real-time dissemination, automated storm tracking, storm trends, and warnings (Lockheed Martin Corporation 1997). In short the WSR-88D has been implemented to provide more accurate and timely warnings. Rain is easy to detect by the typical radar, however its measurement accuracy can depend on the type of precipitation that is occurring. This basic property is the drop size distribution (Marshall and Palmer, 1948), which gives the size of rain as a function of rain rate. This allows scientists to determine the number of drops per unit volume and per unit drop size interval for any raindrop size. Precipitation is estimated using the Z-R relationships, which is a relationship between the rain rate and the radar reflectivity. Z-R relationships are used to derive rainfall totals from radar data. The radar does multiple scan levels to obtain a full storm volume of the atmosphere. However in terms of precipitation data, one cannot be certain that suspended droplets are actually reaching the surface, even though the lowest elevation (0.5 degree) slice is being used (Figure 4). Figure 4. Radar Scan Levels (source: Djurcilov and Pang, 2000) Precipitation does not fall in a perfectly vertical fashion. Depending on the wind directions, rain falls in a slight to significant angle. Thus, rainfall estimation directly beneath droplets at elevation may be an erroneous assumption. Looking at the lowest level will help reduce some of these previous mentioned errors. These individual NEXRAD Scan Angles provide radar slices SOARS 2006, Braxton Edwards, 6

7 through the atmosphere, with each slice corresponding to a NOAA/NWS Base Reflectivity data product. The Composite Reflectivity data products contain the maximum reflectivity value of all layers for a given geographic position. These reflectivity values are derived from dbz values. Of the three primary NEXRAD scan modes, we will be using the precipitation mode. This provides elevation scans every 6 minutes. Rainfall Verification Rineheart (1991) states that it is common to have radar estimates of rainfall and rain gage estimates differ by a factor of two which is 100% error. Current research generally agrees on the specific structure for increasing the accuracy of precipitation estimates via correcting radar estimates based upon the rain gauges with sampling an area of 2.8 x 10 ^-8 sq mi (8 to 12 inches across) below the field. A radar reflectivity value is an average over this 1.5 sq. mi. area giving it a sample area almost 2 million times larger than that or a rain gage [Hoblit, 1999]. The amount precipitation may be above or below by a given amount depends upon several factors, such as type of precipitation and local conditions. The general consensus is that radar precipitation estimation becomes more difficult the further away from the radar the estimate is taken the less likely it is to agree with measurements taken from the ground below. This is due to some of the precipitation evaporating before it reaches the surface [Zawadzki, 1984]. This is also evident in fast moving high precipitation storms due to the fact that it takes rain some time to fall to the earth. Radar measured rain above a gage site might travel some distance from the rain gage before it hits the ground. Overall, the strength of a rain gage is its ability to measure rainfall at a point. The weakness of a gage is unknown as to what is happening in the areas between gages. The strength of radar is its ability to define the spatial variability of rainfall; however its weakness is its relative inability to describe the absolute depth of rainfall consistently at a given location. Comparison of radar and gage measurements of precipitation is shown in Figure 5. SOARS 2006, Braxton Edwards, 7

8 Figure5. Radar vs. Rain Gage comparison (source: Hoblit, 1999) There are several methods for improving rainfall estimates from radar. Most relevant to the research conducted here is the method by Brandes et al. (1998). The general approach in conducting radar/ rain gage analysis involves determining the bias factor between the total gauge estimate and radar estimate over that area. Bias factors over 1.0 depicted underestimation while factors under 1.0 depicted over estimation. The goal is to have both radar and rain gages yielding the same values thus allowing rain gages in the radar field of view transmit data to be integrated into the radar data. This can provide real-time more concrete estimates of rainfall which is crucial information for operational hydrologist and flood forecasters. GIS Geographic Information Systems (GIS) provides a platform where the measurements from both radar and rain gages can be displayed simultaneously, in the same spatial framework, thus allowing for comparison, analysis and mathematical correction of the precipitation estimate. Newest version of ArcGIS 9.2 has a functionality to read netcdf files natively. netcdf is a file format created by Unidata (UCAR) to aid in the process of acquiring, displaying, and analyzing Earth-system data. netcdf provides an effective way to store and retrieve multidimensional scientific data. The netcdf format is useful in the integration with GIS due to its ability in allowing datasets to be transported between dissimilar computers, reducing programming effort in interpreting formats, and reducing errors from misinterpreting data. netcdf is a key format for GIS in that it allows one to contain metadata in the form of dimensions, variables, and attributes. An example of this is a rain gage file containing dimensions of latitude and longitude, variable containing one hour rainfall accumulations, and the associated attribute of units: millimeters. SOARS 2006, Braxton Edwards, 8

9 GIS allows for the linking of meteorological, hydrological, and geographic information all in one display. In combination with scripting language (e.g., Python) GIS becomes a powerful tool in the advent to create models that run many different calculations in one motion in preparation for display. These tools are useful for decision makers who need information from many different sources in a timely manner. Scripting through GIS enables data to be pulled from many different files and linked together in one scripting program. Once this information is displayed in GIS, users will be able to identify areas of interest based upon the layer information. This information may be displayed in either vector (point, line, polygon) or raster (grid) format (Figure 6). Gage Locations 1 hour precip counties UDFCD elevation Value High : 4396 Low : 1020 Figure 6. Representation of raster (elevation) and vector (gage locations) in a GIS. The goal of this research is to conduct spatial analysis and verification of the radarderived precipitation over the UDCFD. Specific objectives include: 1) development of GISbased methodology for radar rainfall verification and 2) identifying key patterns in radar error during convective and stratiform precipitation events. Data and Methods Two main datasets were used in this project: precipitation measurements from the UDFCD tipping bucket rain gage network; and reflectivity measurements from the, National Weather Service WSR-88D radar. Both data sets were available in netcdf format through Research Applications Laboratory (RAL) at NCAR. The radar netcdf data were available in Climate and Forecast (CF) convention, while rain gage data did were not conformed to the CF netcdf convention. Due to limitation in data availability, two days were used to for analysis: June 24, 2006 and July 9, Both days had complete record of gage and radar measurements SOARS 2006, Braxton Edwards, 9

10 and represented two common types of precipitation events: convective (June 24) and stratiform (July 9). In addition, a watershed boundary dataset was used for estimation of precipitation on a watershed level. Radar reflectivity data were measured at 6 min interval, which resulted in about 160 netdcf files per each day. A Python script was created to automate the process of bringing all radar netcdf files into ArcGIS as raster layers (Appendix A). The gage data were brought into ArcGIS manually, due to the fact that the data were not in CF netcfd convention (current standard of netcdf format for ArcGIS) and therefore could not be read directly as feature layers. Rain gage data contained information on the 24-hour precipitation accumulation therefore each day required only one netcdf file. Radar derived precipitation accumulation was calculated using Z-R relationship for lowest level scan. The computation was performed in ArcGIS using tools for analysis of raster layers. Table 1 shows parameters used in calculating precipitation accumulation. Two different Z-R relationships were used for two precipitation events: Marshall-Palmer WSR-88D and Convective. Precipitation accumulation was computed for each time interval of radar measurement and then summed into the 24-hour total accumulation for each day. Table 1. Z-R relationships for convective and stratiform precipitation events. Relationship Equation Optimum For: Marshall-Palmer WSR- (z=200r1.6) General stratiform precipitation 88D Convective (z=300r1.4) Summer deep convection For analysis in GIS it is important to have both layers in a raster format. Gage data were converted from feature format to raster format using two approaches: 1) creating a raster dataset of only those values measured at gage locations, and 2) creating a raster dataset by spatially interpolating between the gages, using the Inverse Distance Weighting (IDW) technique. These two approaches allowed for two types of radar verification: 1) Estimating of mean difference between gage and radar measurements and correcting radar data based on this mean value 2) Estimating mean difference using IDW surface and radar measurements and correcting radar based on those values. To estimate average precipitation values in watersheds, spatial statistics tool (i.e., zonal statistics) was used for both raster gage and radar data layers. Results Case 1: June 24 th Convective Precipitation Event The 24 th of June was a convective event over the UDFCD. This precipitation event was associated with a significant amount of hail as well as extreme downpours (Figure 7). The radar coverage for this area experienced an average overestimate of precipitation values for the extent of the event. Hail typically does give a higher estimate of rainfall that what actually occurs. This is why it is critical to have onsite observers to report back measured precipitation amounts on the ground. Gage estimates differed from Radar on average from.75 in. to -1.5 in., while SOARS 2006, Braxton Edwards, 10

11 IDW estimates differed on the order of.5 in. to -2.5 in. from the radar (Figure 8). Watershed averaged precipitation values are shown in Figure 9. Gage Radar IDW (a) (b) (c) Figure 7. Gage (a), Radar (b) and IDW-interpolated surface precipitation accumulations. SOARS 2006, Braxton Edwards, 11

12 G-R IDW-R (a) (b) Figure 8. Gage and IDW Differences for G-R(a) and IDW-R(b). Radar Gage IDW SOARS 2006, Braxton Edwards, 12

13 (a) (b)top (c)bottom Figure 9. Watershed averaged precipitation accumulation for Gage(a), Radar(b), IDW(c). June 24 Statistics In terms of a 24 hour span, the difference between the gage and radar measurements on this day where small (Figure 10). This could be due to the fact that the spatial distribution of rainfall over the gage sites was also favorable for accurate radar measurement as well. Also, there were no significant rain rates or intense updrafts to affect the rain accumulations positively or negatively. The IDW measurement difference between that of the radar was actually significantly more than that of the radar alone. One must also take into consideration that the interpolation is a mathematical calculation. Thus when taking this into account for non-gage regions a 3 mm difference in measurements is a relatively good approximation (Figure 11). Figure 10. Difference between gage and radar measurements for June 24 th. Figure 11. IDW Difference between radar for June 24 th. SOARS 2006, Braxton Edwards, 13

14 With the number of gage and radar measurements in unison, we were able to determine the accuracy of radar measurements for specific indices. On average the radar underestimate varied by 8 mm (Figure 12) and overestimated by 3.8 mm (Figure 13) which is within typical error regimes Figure 12. Number of radar underestimates for June 24 th. th Figure 13. Number of radar overestimates for June 24. The Gage to Radar ratio is another form of telling one whether or not the Radar is underestimating the precipitation or not. In general for this perspective the radar grossly underestimated the amount of precipitation that was occurring as apposed to the average difference (Figure 14). SOARS 2006, Braxton Edwards, 14

15 Figure 14. Gage to Radar ratio for June 24 th. In terms of total accumulation, the rain gage and the radar values obtained almost the same amount of accumulation, which is good if one is using radars to determine the regional total water budget in terms of precipitation (Figures 15 and 16). The regional coverage of the radar was mapped exactly with that of the radar to eliminate the error involved in precipitation estimates from radar estimates alone. Figure 15. Total Rain gage accumulation for June 24 th. SOARS 2006, Braxton Edwards, 15

16 Figure 16. Total radar accumulation for June 24 th. The general statistics for June 24 th (Table 2) depicted reasonable results in terms of relative dispersion of the data. On average the Gage and Radar values differed by 2 mm when measuring precipitation at the same point. In terms of total precipitation accumulations, the radar did measure more precipitation. However one must consider that this was a hail event, which would also account for higher precipitation accumulations from the radar. Table 2: June 24 th statistics. Date # of gages Storm Scans Average precipitation gage June Total Precipitation Gage Average precipitation radar/extent Total precipitation radar matched to gage relative dispersion about G/R Average G/R G-R Max G-R Average IDW Difference Case 2: July 9 th, Stratiform Precipitation For the July 9 th event, the radar did a reasonable job of not overestimating the rainfall (Figure 17), but it did however have gross underestimates in many areas of the domain (Figure 18). These are good measurements due to the fact that the average overestimate is around half an inch. SOARS 2006, Braxton Edwards, 16

17 Figure 17. Total radar overestimates July 9 th. Figure 18. Total radar underestimates July 9 th. In terms of regional precipitation, radar underestimated the total accumulation for the region (Figure 19). This may be attributed to the off an on nature of the precipitation throughout the day. Although it may have been a stratiform event, it was also generally isolated in its nature. SOARS 2006, Braxton Edwards, 17

18 IDW Gage Radar (a) (b) (c) Figure 19. IDW- interpolated surface (a) Gage,(b) and Radar (c) precipitation accumulation. When looking at the zonal statistics (Figure 20) for the event, both the Gage and the IDW maps indicated higher precipitation contrasts in the NE and SE portions of the UDFCD as apposed to the isolated accumulations NW of Golden, CO. Gage IDW Radar SOARS 2006, Braxton Edwards, 18

19 (a) (b),(c) Figure 20. Watershed averaged precipitation accumulation for Gage(a), IDW(b), and Radar (c). The average difference results from both methods were expected due to the vast dissimilarities in precipitation fields between the Gage and IDW values as apposed to the radar values. The radar did not handle precipitation changes well along the NW and SW portions of the UDFCD, which shows in the error plots for this day (Figure 21). Gage-R IDW-R (a) (b) Figure 21. Gage(a) and IDW(b) difference maps for July 9 th. June 9 th Statistics The radar accumulation fields for this day did not match up well with the rain gage network measurements (Figures 22, 23, 24). This may be a function of the locality of the storms. Areas of high precipitation may have been directly over gage sites, and thus the radar would average out these areas of high precipitation. The average radar accumulation was 11 mm, but the rain gage was only 9 mm. However the difference values between the gage and the radar for the entire spatial domain were on average 11 mm. These positive results show that even though the radar has a higher precipitation values as a whole, in areas of gage measurements the radar underestimated the amount of precipitation actually reaching the ground. SOARS 2006, Braxton Edwards, 19

20 Figure 22. Radar accumulation for July 9 th. Figure 23. Gage accumulation minus the radar accumulation for July 9 th. Figure 24. Gage accumulation for July 9 th. SOARS 2006, Braxton Edwards, 20

21 In terms of overall ratio, there was significant error in areas where gages recorded large amount of precipitation while the radar average over that area yielded a small precipitation value, thus driving the ratio values into gross underestimates in the upper 400 percent range as shown in Figure 25. Figure 25. Gage to radar ratio for July 9 th. In terms of general statistics for July 9 th, the total precipitation measured by the radar was greater than that measured by the gage network (Table 3). However the relative dispersion for the entire data set was minimal. On average the Gages overestimated the rainfall, while only in a few areas (i.e, NW of Golden) there were significant radar overestimates of rainfall. Table 3. July 9 th Statistics. Date # of gages Storm Scans 9-Jul Total Precipitation Radar relative dispersion about G/R Total Precipitation Gage Average G/R G-R Overestimate: Max G-R Underestimate: Max, average Average Precipitation Gage Average Precipitation Radar IDW Difference G-R Overestimate Average G-R Underestimate Average Gage Difference In general, the radar did perform better on the convective day due to the isolated nature of the event. There was more uniform agreement between precipitation areas and non precipitation areas. For July 9th, the precipitation fields covered a much lager area, in addition to having isolated pockets of precipitation which the radar may have averaged out. In terms of G/R ratio variation from different studies (Brandes and Wilson, 1979) found that on average G/R ratio varied from 10.5 mm to over 61 mm. SOARS 2006, Braxton Edwards, 21

22 Conclusions In this study a GIS-based method was developed and implemented to analyze and verify spatial patterns of rainfall measured from radar and rain gages. Both radar and gages have their advantages and disadvantages for accurate measurements of rainfall. In taking a hydrological perspective for this study, the underlying assumption was that rain gages produce more accurate measurements and can serve as a ground truth for radar corrections. Data from two rainfall events showed that radar overestimated accumulation in areas of intense precipitation for both cases. In terms of overall average differences, the gage averages contained the smallest average differences as apposed to using the IDW averages. This was found to be a function of the error in the mathematical nature of the IDW method because it is difficult to predict data in areas of no observational records. In terms of climatological work and improved methodology, areas of interest may be in developing trends of radar under/overestimates over a particular area for different storm types, precipitation amounts, wind characteristics, and other meteorological factors. The implementation of radar rainfall verification in a GIS is an important step in the flood warning process. This tool allows planers to view historical system responses to varying storm types and durations. The meteorological results can further be combined with hydrological and socioeconomic information, thus allowing emergency management and flood control engineers to obtain a complete picture of the environment. Acknowledgements I would like to thank my Science Mentors Olga Wilhelmi and David Yates and my Writing and Communication Mentor Cindy Worster for their guidance throughout this project. I would also like to thank Jennifer Boehnert for her help in technical support, and Ed Brandes for providing key information. I am grateful to have worked with such talented and devoted scientist. I thank you all for allowing me to work under your supervision this summer, and I have learned so much from each of you. I thank you for the time that you have shared with me. Braxton Lee Edwards: Senior Meteorology Major University of Oklahoma SOARS 2006, Braxton Edwards, 22

23 References Apaydin H., Sonmez F., and Yildirim Y.(2004), Spatial interpolation techniques for climate data in the GAP region in Turkey, Climate Research., 28, Brandes E., Vivekanandan J., and Wilson J. (1998), A comparison of radar reflectivity estimates of rainfall from collocated radars, Oklahoma University Press, Journal of Atmospheric and Oceanic Technology 16, Brandes E., Wilson J. (1979), Measuring storm rainfall by radar and rain gage instruments and techniques for thunderstorm observation and analysis Cambridge Bay Weather (2005) URL (visited June 10, 2006) Chang KT. (2004) Introduction to geographic information systems, McGraw-Hill Companies Curtis D., Clyde B. (1999), Comparing spatial distribution of rainfall derived from rain gages and radar. Journal of Floodplain Management, NEXRAIN corporation pg 1-7. Dirks KN., Hay JE., Stow CD., Harris D. (1998), High-resolution studies of rainfall on Norfolk Island. Part 2: Interpolation of rainfall data, J Hydrol 208(3-4): Djurcilov S. and Pang A., Visualizing Sparse Gridded Data Sets, IEEE Computer Graphics and Applications, IEEE Computer Society Press, Los Alamitos, CA, September / October 2000, Franke R. (1982), Smooth interpolation of scattered data by local thin plate splines. Computers and Mathematics with Applications 8: Hoblit B. (1999), spatial scale data requirements using NEXRAD (WSR-88D) for accurate hydrologic prediction in urban watersheds M.S. Diss., Rice University. Lockheed Martin Corporation (1997), NEXRAD WSR-88D design innovation the world over Radar & Sensor Systems. Marshall J., Palmer W. (1948), The distribution of raindrops with size Journal Meteorology 5, Naoum S., Tsanis I.K. (2004), Ranking spatial interpolation techniques using a GISbased DSS. Global Nest: the Int. J. 6, 1, Rinehart R. (1991), Radar for meteorologist, Department of Atmospheric Sciences University of North Dakota Urban Drainage & Flood Control District (2005) URL _history.htm (visited June 10, 2006). Zawadzki, I. (1984), Factors affecting the precision of radar measurements of rain, Preprints, 22d Conf. on Radar Meteorology, Zurich, Switzerland, Amer. Meteor. Soc., SOARS 2006, Braxton Edwards, 23

24 Appendix A Script 1: SOARS 2006, Braxton Edwards, 24