Full report

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NASA/TM—2018–219882 A Rain Taxonomy for Degraded Visual Environment Mitigation P.N. Gatlin and W.A. Petersen Marshall Space Flight Center, Huntsville, Alabama March 2018

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The NASA STI Program…in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the lead center for NASA’s scientific and technical information. The NASA STI Program Office provides access to the NASA STI Database, the largest collection of aeronautical and space science STI in the world. The Program Office is also NASA’s institutional mechanism for disseminating the results of its research and development activities. These results are published by NASA in the NASA STI Report Series, which includes the following report types: • TECHNICAL PUBLICATION. Reports of completed research or a major significant phase of research that present the results of NASA programs and include extensive data or theoretical analysis. Includes compilations of significant scientific and technical data and information deemed to be of continuing reference value. NASA’s counterpart of peerreviewed formal professional papers but has less stringent limitations on manuscript length and extent of graphic presentations. • TECHNICAL MEMORANDUM. Scientific and technical findings that are preliminary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minimal annotation. Does not contain extensive analysis. • CONTRACTOR REPORT. Scientific and technical findings by NASA-sponsored contractors and grantees. • CONFERENCE PUBLICATION. Collected papers from scientific and technical conferences, symposia, seminars, or other meetings sponsored or cosponsored by NASA. • SPECIAL PUBLICATION. Scientific, technical, or historical information from NASA programs, projects, and mission, often concerned with subjects having substantial public interest. • TECHNICAL TRANSLATION. English-language translations of foreign scientific and technical material pertinent to NASA’s mission. Specialized services that complement the STI Program Office’s diverse offerings include creating custom thesauri, building customized databases, organizing and publishing research results…even providing videos. For more information about the NASA STI Program Office, see the following: • Access the NASA STI program home page at http://www.sti.nasa.gov • E-mail your question via the Internet to help@sti.nasa.gov • Phone the NASA STI Help Desk at 757 –864–9658 • Write to: NASA STI Information Desk Mail Stop 148 NASA Langley Research Center Hampton, VA 23681–2199, USA

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NASA/TM—2018–219882 A Rain Taxonomy for Degraded Visual Environment Mitigation P.N. Gatlin and W.A. Petersen Marshall Space Flight Center, Huntsville, Alabama National Aeronautics and Space Administration Marshall Space Flight Center • Huntsville, Alabama 35812 March 2018 i

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Available from: NASA STI Information Desk Mail Stop 148 NASA Langley Research Center Hampton, VA 23681–2199, USA 757–864–9658 This report is also available in electronic form at http://www.sti.nasa.gov ii

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EXECUTIVE SUMMARY This Technical Memorandum (TM) provides a description of rainfall for the purpose of degraded visual environment (DVE) mitigation. The taxonomy is based on raindrop size measurements collected around the globe and encompasses several different climate types. Included in this TM is a description of the rainfall observations considered, an explanation of methods used to process those data, and resultant metrics comprising the weather taxonomy database. For purposes of DVE mitigation, rain can be described using three categories that correspond to light, moderate, and heavy amounts of liquid water, and these are related to traditional rainfall intensity-based definitions. Each of the categories in the rain taxonomy are characterized by a unique set of raindrop sizes that can be used in simulations of electromagnetic wave propagation through a rain medium. This taxonomy defines the size distributions for light, moderate, and heavy rainfall. Light rain consists of raindrops with an average mass-weighted mean diameter (Dm) of 0.9 mm, moderate rain consists of raindrops with an average Dm of 1.1 mm, and heavy rain consists of raindrops with an average Dm of 1.6 mm. A description of the relational database containing the weather taxonomy built for DVE mitigation is provided in a companion report, “A Weather Taxonomy Database for DVE Mitigation.” iii

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iv

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TABLE OF CONTENTS 1. GENERAL RAINFALL CHARACTERISTICS ............................................................... 1 1.1 Raindrop Shape ............................................................................................................ 2 1.2 Raindrop Fall Speed ..................................................................................................... 3 2. CONSTRUCTION OF THE RAIN TAXONOMY ........................................................... 4 2.1 Defining the Raindrop Size Distribution ....................................................................... 6 2.2 Model to Describe Rain: Gamma Distribution ............................................................. 7 2.3 Definition of Rain Taxonomy Metrics .......................................................................... 7 3. TAXONOMY OF RAIN .................................................................................................... 9 REFERENCES ....................................................................................................................... 13 v

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LIST OF FIGURES 1. Distribution of rainfall intensities from 133,000 min of rainfall observations used to define the rain taxonomy described in this TM. Rain in any climate always exhibits such a skewed distribution, which indicates that low intensity rain is the most frequent type of rain observed ........................................................... 1 2. Shapes of falling raindrops with 1, 2, 3, 4, 5, and 6 mm diameter compared with their equivalent spherical shape. Falling raindrops larger than 1 mm in diameter tend to take on a more oblate shape but with a flattened base .................. 2 3. Map showing locations (small boxes) of 2DVD rainfall observations that were used to define the rain taxonomy. The colors represent Earth’s climates according to the Köppen climate classification system ................................................ 4 4. An example of the 2DVD (foreground—third generation compact type; background—second generation low-profile type), which is the type of disdrometer that was used to construct the weather taxonomy for rain described herein .......................................................................................................... 5 5. A 3D representation of the rain taxonomy that shows three categories of rain exhibiting different physical rainfall characteristics. This plot is in terms of the DVE rain taxonomy metrics (sec. 2.3) ............................................................... 10 6. Distributions of RSD metrics that define the rain taxonomy for the three categories of rain: (a) Plot of Dm, which is the RSD metric that represents characteristic raindrop diameter and (b) plot of NT, which is the RSD metric of the total raindrop concentration ............................................................................. 11 vi

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LIST OF TABLES 1. Overview of rainfall observations used to define the rain taxonomy. The color shading corresponds to the climate classification map in figure 3 ................................ 6 2. Definition of rainfall types in this taxonomy with mean and standard deviation raindrop diameter ....................................................................................................... 9 3. Statistical description of the raindrop size distribution model parameters for light rain defined by LWC < 0.09 g/m3 ................................................................... 11 4. Statistical description of the raindrop size distribution model parameters for moderate rain defined by 0.09 ≤ LWC < 0.4 g/m3 ................................................... 12 5. Statistical description of the raindrop size distribution model parameters for light rain defined by LWC ≥ 0.04 g/m3 ................................................................... 12 vii

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LIST OF ACRONYMS 2DVD two-dimensional video disdrometer DVE degraded visual environment GPM Global Precipitation Measurement LWC liquid water content RSD raindrop size distribution TM Technical Memorandum VIS visibility viii

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NOMENCLATURE a semi-major (axis) b semi-minor (axis) D equivalent spherical diameter Dm mass-weighted mean diameter i index of the size bin N number of raindrops NT total drop concentration n number of diameter bins R rainfall intensity v velocity μ shape parameter of the gamma distribution model ρw density of liquid water ix

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x

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TECHNICAL MEMORANDUM A RAIN TAXONOMY FOR DEGRADED VISUAL ENVIRONMENT MITIGATION 1. GENERAL RAINFALL CHARACTERISITCS Precipitation in the form of liquid water drops can be classified as either rain or drizzle based on the drop diameter. The Glossary of Meteorology defines raindrops as having diameters of 0.5 mm or larger, whereas water drops smaller than 0.5 mm but larger than 0.1 μm in diameter are referred to as drizzle drops.1 Rain observed in nature has a wide range of intensities, typically ranging from 0.01 mm/hr (<0.04 in/hr) to just over 300 mm/hr (>11.8 in/hr). The vast majority of the time that rain occurs it occurs at the lower end of this range, with the median rain rate being approximately 0.8 mm/hr (fig. 1). Rainfall rates exceeding 10 mm/hr (0.4 in/hr) are not nearly as frequent or long lasting. Although weaker rainfall intensities occur for longer periods of time, there are some climates where intense rainfall is relatively more frequent (e.g., tropical climates), but the distribution of rain is always skewed toward lower intensities. 0.25 0.2 0.15 0.1 Relative Frequency 0.05 0 1 n=133,000 0.8 Cumulative Probability 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Rainfall Rate (mm/hr) Figure 1. Distribution of rainfall intensities from 133,000 min of rainfall observations used to define the rain taxonomy described in this TM. Rain in any climate always exhibits such a skewed distribution, which indicates that low intensity rain is the most frequent type of rain observed. 1

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1.1 Raindrop Shape Raindrop sizes range from 0.5 mm to just under 10 mm in diameter (diameter being that of its equivalent spherical volume since raindrop shape can vary). Falling raindrops larger than 1 mm in diameter become less spherical and tend to take on a more oblate (i.e., vertically compressed) shape similar to that shown in figure 2. One of the most simplistic descriptions of raindrop shape in terms of its size is given by the length of its semi-minor, b, axis to that of its semi-major, a, axis: b = 1.03 − 0.062D , (1) a is its equivalent spherical diameter in units of millimeters.3 More detailed rainwhere b > a and D drop shape models exists that can provide a surface contour of a raindrop.4 5 3 2 1 Figure 2. Shapes of falling raindrops with 1, 2, 3, 4, 5, and 6 mm diameter compared with their equivalent spherical shape.2 Falling raindrops larger than 1 mm in diameter tend to take on a more oblate shape but with a flattened base. 2 F2_1803

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1.2 Raindrop Fall Speed Natural raindrops attain terminal fall velocities that range from 2 m/s for diameters of 0.5 mm to 7 m/s for those around 2 mm diameter and asymptotically approach 9 m/s for drops exceeding 4 to 5 mm in diameter.5 A commonly used equation for computing terminal velocity, 6 v (m/s), of natural raindrops falling in still air as a function of equivalent spherical volume diameter, D (mm), is: 10.3exp(0.6D) . (2) v = 9.65 − It should be noted that raindrop terminal velocity increases with altitude and the result of the above equation should be adjusted accordingly with height above minimum sea level.7 3

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1. CONSTRUCTION OF THE RAIN TAXONOMY Raindrop size measurements from 14 locations encompassing eight different climates were considered (see fig. 3). These measurements were obtained using two-dimensional video disdrometers (2DVDs; cf., fig. 4) that supported NASA’s Global Precipitation Measurement (GPM) Mission.8 This type of instrument provides a measure of particle size, shape, and fall speed by employing two line-scan cameras that perpendicularly view a pair of illuminated optical planes 2 vertically offset about 6.7 mm over a sample area of 100 cm . The 2DVD measures particles with a resolution of 0.2 mm for diameters as small as 0.3 mm and their associated vertical velocity to within 4% accuracy.9 As a result, the 2DVD is commonly used as a reference for evaluating the accuracy of other disdrometers.10–12 Hence, the taxonomy defined in this Techncial Memorandum (TM) was derived from the most comprehensive characterization of rainfall to date. 90 N 45 N 0 180 W 135 W 90 W 45 W 0 45 S 90 S 45 E 90 E 135 E 180 E Af Am As Aw BWh BWk BSh BSk Csa Csb Csc Cwa Cwb Cwc Cfa Cfb Cfc Dsa Dsb Dsc Dsd Dwa Dwb Dwc Dwd Dfa Dfb Dfc Dfd ET EF First Letter Second Letter Third Letter A: Tropical f: Fully Humid T: Tundra h: Hot arid B: Dry m: Monsoon F: Frost k: Cold arid C: Mild Temperate s: Dry Summer a: Hot Summer D: Snow w: Dry Winter b: Warm Summer E: Polar W: Desert c: Cool Summer S: Steppe d: Cold Summer Data source: Terrestrial Air Temperature/Precipitation: 1900–2010 Gridded Monthly Time Series (V 3.01) Resolution: 0.5 Degree Latitude/Longitude Web Site: http://hanschen.org/koppen Ref: Chen, D. and H.W. Chen, 2013: Using the Köppen classification to quantify climate variation and change: An example for 1901–2010. Environmental Development, 6, 69–79, 10.1016/j/envdev.2013.03.007. Figure 3. Map showing locations (small boxes) of 2DVD rainfall observations that were used to define the rain taxonomy. The colors represent Earth’s climates according to the Köppen climate classification system.13 4

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Figure 4. An example of the 2DVD (foreground—third generation compact type; background—second generation low-profile type), which is the type of disdrometer that was used to construct the weather taxonomy for rain described herein. Table 1 provides an overview of the locations of the raindrop size measurements that were used to define the rain taxonomy described in this TM. This rain taxonomy represents the characteristics of rainfall for 8 of the 31 climate types defined in the Köppen climate classification system. The Köppen system classifies the world’s climates based on temperature and precipitation13 and is one of the most widely used climate classification schemes. From table 1 it is evident that the vast majority of the raindrop size observations were obtained in Huntsville, Alabama. Furthermore, the climate type of Huntsville (Köppen climate classification is Cfa13), which can be described as having mild temperatures throughout the year and being very humid with hot summers, is the mostF4_1803 represented climate contained in this rain taxonomy since it was sampled in six different locations. 5

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Table 1. Overview of rainfall observations used to define the rain taxonomy. The color shading corresponds to the climate classification map in figure 3. Climate (Köppen) Dates of Number of Location Description Observations 1-Minute RSDs Cfa: mild temperate, fully humid, hot summer July 2007 – December 2013 133,803 Huntsville, Alabama, USA Cfb: mild temperate, fully humid, warm summer October 2015 – January 2016 69,147 Quinault, Washington, USA December 2011 – November 2013 52,706 Manus Island, Papua, New Guinea Af: tropical rainforest November 2005 –April 2007 38,711 Koto Tabang, West Sumatra, Indonesia Af: tropical rainforest Aw: tropical savannah with dry winter March 2011– November 2013 35,726 Darwin, Australia Cfa: mild temperate, fully humid, hot summer June 2012 – December 2013 33,123 Wallops Island, Virginia, USA Cfa: mild temperate, fully humid, hot summer March 2011 – November 2013 32,675 Billings, Oklahoma, USA Dfa: snow, fully humid, hot summer April 2013 – June 2013 27,905 Eastern Iowa, USA Cwa: mild temperate with dry winter, hot summer August 2011 – September 2015 27,700 Daegu and Bosung, South Korea Cfa: mild temperate, fully humid, hot summer July 2003 – November 2003 19,857 Hiratsuka, Japan Cfa: mild temperate, fully humid, hot summer November 2003 – May 2004 14,335 Okinawa, Japan July 2005 – January 2006 11,672 Mayaguez, Puerto Rico Am: tropical monsoon Cfa: mild temperate, fully humid, hot summer April 2014 – June 2014 11,587 Asheville, North Carolina, USA August 2004 – June 2005 11,333 San Juan, Puerto Rico Af: tropical rainforest Dfb: snow, fully humid, warm summer November 2006 – May 2007; 9,591 Barrie, Ontario, Canada October 2011 – March 2012 Several of the 2DVD datasets, such as those from Washington, Iowa, and Ontario, were obtained for only a single season as part of a NASA GPM field campaign.14 Hence, the information provided for those locations where only a few months of observations exist may not be as representative of all possible weather regimes occurring in their respective climates. For instance, the taxonomy may not be as representative for rain occurring in climates classified as Am, Cfb, Dfa, and Dfb as it is for those climates where at least several seasons were sampled (e.g., Af, Cfa, Cwa). 2.1 Defining the Raindrop Size Distribution The individual raindrops measured by the 2DVD for locations in table 1 were checked to ensure that equivalent spherical diameters ranged from 0.3 to 10 mm and drop fall speeds were within ±40% of the expected terminal fall velocity,6 which helps mitigate inclusion of non-rain particles or incorrect particle matches that can result from the 2DVD processing software.15 Raindrops that passed these constraints were counted over 1-min intervals and apportioned into 0.2-mm-diameter-size bins to obtain a sample of the raindrop population. Each bin with rain was required to contain at least two raindrops and each 1-min sample was required to contain at least 10 raindrops total. These additional requirements facilitated a representative sample for the curvefitting procedure used to obtain a better estimate of the 1-min raindrop population across the full spectrum of raindrop diameters while allowing a robust number of samples to define the taxonomy. The 1-min binned raindrop observations likely do not include the full spectrum of diameters in the raindrop population falling during the 1-min sample collection due to the variability of rainfall size distributions and issues with sampling such a population using such a small measurement 6

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area (i.e., 2DVD only samples across a 10 cm × 10 cm area). Hence, to better depict the actual raindrop population, a distribution with known properties was used to define the raindrop size distribution (RSD). RSDs have been defined using either an exponential, gamma, or log-normal distribution.16–18 Each one has its strengths and weaknesses, but raindrop populations sampled with 2DVDs have been shown to closely resemble a gamma distribution19–21 and this is the type used to define the rain metrics of this weather taxonomy. 2.2 Model to Describe Rain: Gamma Distribution The gamma model formulation used to define the rainfall characteristics contained within this weather taxonomy is commonly referred to as the gamma drop size distribution. It is used to compute the number of raindrops, N, of diameter D within a volume of air: N T N(D) = D m m with μ +1 ⎛ D ⎞ f ⎜ ⎟ , (3) μ ⎝ D ⎠ μ ⎛ D ⎞ (4 + μ) ⎛ D D f ⎜ ⎟= ⎜ μ ⎞ ⎡ ⎤ ⎟ exp ⎢−(4 + μ) ⎥ , (4) ⎝ D ⎠ Γ(μ +1) ⎝ D ⎠ ⎣ D ⎦ m m m where NT is the total drop concentration, Dm is the mass-weighted mean diameter, and μ is the shape parameter of the gamma distribution. These three parameters should be used within the model given by equation (3) to obtain the raindrop size distribution. Both Dm and NT were computed from the 1-min binned raindrop samples and the μ was determined via minimizing the difference between the observed N(D) and the model given by equation (3) following reference 22. This resulted in 561,616 min of rainfall (i.e., raindrop size distributions) that were used to determine the physical characteristics of different types of rain. 2.3 Definition of Rain Taxonomy Metrics The primary metric used to define rain for this taxonomy is the liquid water content (LWC) (related to the third moment of the raindrop size distribution) which provides a measure of the mass of liquid water per unit volume of air. Hence, LWC is a metric that can be used for determining signal loss due to rain. It is defined in this taxonomy as 50 πρ w 3 LWC = ∑ D N D( )dD , (5) 6 i=1 i i i where ρ is the density of liquid water (=106 g/m3 at 4 °C) and the summation is performed over w n number of diameter bins with width dD (0.2 mm bin sizes were used for the LWC reported in this taxonomy). The units of LWC used in this taxonomy are g/m3. 7

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The characteristics size of the RSD is given by the mass-weighted mean diameter, Dm, which is defined in this taxonomy as n 4 ∑ D N D( )dD i=1 i i i D = m n . (6) 3 ∑ D N D( )dD i=1 i i i The units of Dm in this taxonomy are mm. The total drop concentration, NT, is defined in this taxonomy as 6 LWC Γ(μ +1) 3 N = T 3 (4 + μ) . (7) πρ D Γ(μ + 4) w m –3 The units of NT in this taxonomy are m . This metric is commonly referenced in logarithmic units but must be in linear units when used to compute N(D) in equation (3). Visibility is another metric that is commonly used in aviation. For purposes of this taxonomy, visibility is based on 550 nm wavelength, which is that seen with the unaided human eye. Hence, visibility represents the visual range of objects seen with a contrast of 5.5% against the background horizon sky.23 It is defined in this taxonomy as ⎞ D ⎛ 2.9 VIS = m (8) ⎝ 3.9⎠ 1.04 LWC is mm and LWC is g/m3. This formulation is based on that with units of kilometers given that Dm given in reference 24 and assumes a Marshall-Palmer type RSD.16 8

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1. TAXONOMY OF RAIN The function of this taxonomy is to provide a comprehensive set of metrics that define physical characteristics of rainfall types observed in nature. Instead of using rain intensity to define the types of rain observed in nature, LWC was used since it provides a more robust measure of the physical rainfall characteristics and readily facilitates computations requiring signal loss through rain. This taxonomy uses similar qualitative descriptors of rainfall like those based on its intensity—light, moderate, and heavy. However, the rainfall categories used for this taxonomy are based on the LWC. These LWC categories are associated with the light, moderate, and heavy rainfall intensities defined in the Federal Meteorological Handbook on Surface Weather Observations and Reports,25 which is the most commonly used definition of rain reported at airports throughout the United States. Table 2 defines these categories in terms of LWC and maps them to the commonly used rainfall intensity definitions. For example, light rainfall is defined in this taxonomy as having an LWC < 0.09 g/m3 and that corresponds to a rainfall rate less than 2.54 mm/hr. The raindrop diameters reported in table 2 represent the average and standard deviation of Dm within a given category and cannot be used to define the bounds of all raindrop sizes within a given category. Instead, it represents characteristic raindrop sizes in each category. The visibility in table 2 was computed using the corresponding Dm and LWC via equation (8). Table 2. Definition of rainfall types in this taxonomy with mean and standard deviation raindrop diameter. Raindrop Diameter Defining Metric: Descriptive Liquid Water Rainfall Intensity* Visibility (Dm) ± σD m Rainfall Category Content (g/m–3) (mm/hr) (km) (mm) Light LWC < 0.09 R < 2.54 VIS > 9.6 0.9 ± 0.3 Moderate 0.09 ≤ LWC < 0.4 2.54 ≤ R < 7.62 9.6 ≤ VIS < 2.6 1.1 ± 0.4 Heavy LWC ≥ 0.4 R ≥ 7.62 VIS ≤ 2.6 1.6 ± 0.5 Federal Meteorological Handbook.25 * Rain intensity definitions are based on that given by the 9

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The taxonomy herein categorizes the rain using similar qualitative terms but these categories are based on a statistical analysis of raindrop size distribution measurements and therefore connects the qualitative description of rain to its quantitative-based physical characteristics. To do this, a cluster analysis was performed via the K-means technique26 on the 1-min RSDs using the three metrics—LWC, Dm, and NT. A random subset of 9,500 RSDs from each location was used in the cluster analysis to ensure the resultant clusters were not biased towards certain locations/ climates that contained a larger sample of rainfall (e.g., Huntsville, AL and S. Korea). Figure 5 shows the resultant three clusters that correspond to the categories in terms of LWC, Dm, and NT (i.e., a 3D RSD parameter diagram). The light rainfall category (i.e., low LWC) is comprised of small raindrops in relatively small concentrations (i.e., widely dispersed), whereas the heavy rainfall category (i.e., high LWC) contains larger and more numerous raindrops. This trend agrees with the conceptual model of rainfall types; hence, the analysis is sound and the resultant rain taxonomy correctly describes different types of rainfall observed in nature. 8 6 ) –3 4 LWC (g/m 2 0 6 5 4 3 log N (m–3) 10 T 2 1 0 0 1 Light Moderate Heavy 4 5 3 2 Dm (mm) Figure 5. A 3D representation of the rain taxonomy that shows three categories of rain exhibiting different physical rainfall characteristics. This plot is in terms of the DVE rain taxonomy metrics (sec. 2.3). A statistical summary of the rain taxonomy RSD metrics for light, moderate, and heavy rain is shown in figure 6. These distributions represent metrics describing the parameters of the raindrop size distribution model (see sec. 2.2) used to define the three categories within this rain taxonomy. The characteristic diameter shown in figure 6(a) (i.e., Dm) indicates two distinct populations—one characterized by mostly small raindrops associated with light to moderate rain and one characterized by larger drops that occur with heavy rain. As for the total raindrop concentration metric, NT, it can span several orders of magnitude; hence, it is commonly referenced in logarith- F5_1803 mic units. Figure 6(b) shows three distinct populations exist for NT—one consisting of mostly 10

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0.3 1 Light 0.9 Cumulative ProbabilityModerate Cumulative Probability 0.25 Moderate 0.8 Heavy 0.7 0.2 0.6 0.15 0.5 0.4 0.1 Relative Frequency 0.3 0.2 0.05 0.1 0 0 0 1 2 3 4 5 (a) Dm (mm) 0.2 1 Light 0.9 0.8 0.15 Heavy 0.7 0.6 0.1 0.5 0.4 Relative Frequency 0.3 0.05 0.2 0.1 0 0 0 1 2 3 4 5 (b) log N (m–3) 10 T Figure 6. Distributions of RSD metrics that define the rain taxonomy for the three categories of rain: (a) Plot of Dm, which is the RSD metric that represents characteristic raindrop diameter and (b) plot of NT, which is the RSD metric of the total raindrop concentration. low concentrations of raindrops found with light rain, another population consisting of much higher concentrations of raindrops found with moderate rain, and one population with a very high concentration of raindrops that occurs with heavy rainfall. Tables 3–5 contain the three RSD model parameters required to compute the raindrop size distribution given by equation (3) for light, moderate, and heavy rainfall. The tables provide a statistical desciption of LWC and representative Dm, NT, and μ for each rain type within the taxonomy. Additional descriptive statistics for these parameters, such as mean and standard deviation for each rain type and statistics for each climate type, are contained within the companion weather taxonomy database. Some uses of the information contained within tables 3–5 can be used to perform F6_1803 electromagnetic propagation simulations or assess performance of sensors or rainfall simulations relative to this rain taxonomy. Table 3. Statistical description of the raindrop size distribution model parameters for light rain defined by LWC < 0.09 g/m3. (mm) N (m–3) μ LWC Statistic Dm T 5th Percentile 0.84 26 12.6 10th Percentile 0.85 27 12.4 25th Percentile 0.86 31 12 50th Percentile 0.93 57 10.1 75th Percentile 1.03 106 7.4 90th Percentile 1.26 110 4.8 95th Percentile 1.42 111 3.8 11

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Table 4. Statistical description of the raindrop size distribution model parameters for moderate rain defined by 0.09 ≤ LWC < 0.4 g/m3. (mm) N (m–3) μ LWC Statistic Dm T 5th Percentile 0.83 281 10.3 10th Percentile 0.9 280 8.9 25th Percentile 1.03 305 6.5 50th Percentile 1.24 328 4.3 75th Percentile 1.29 473 3.9 90th Percentile 1.32 617 3.8 95th Percentile 1.35 618 3.6 Table 5. Statistical description of the raindrop size distribution model parameters for light rain defined by LWC ≥ 0.04 g/m3. (mm) N (m–3) μ LWC Statistic Dm T 5th Percentile 1.19 933 5.1 10th Percentile 1.35 827 4 25th Percentile 1.45 764 3.4 50th Percentile 1.56 869 3.6 75th Percentile 1.7 1,081 3.2 90th Percentile 1.99 1,550 1.8 95th Percentile 2.09 1,991 1.4 12

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REFERENCES 1. American Meteorological Society, “Rain,” Glossary of Meteorology, April 25, 2012, <http:// glossary.ametsoc.org/wiki/rain>. Accessed: January 1, 2016. 2. Beard, K.V.; and Chuang, C.: “A New Model for the Equilibrium Shape of Raindrops,” J. Atmos. Sci., Vol. 44, No. 11, pp. 1509–1524, <https://doi.org/10.1175/1520-0469(1987)044 <1509:ANMFTE>2.0.CO;2>, June 1987. 3. Pruppacher, H.R.; and Beard, K.V.: “A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air,” Q. J. R. Meteorolog. Soc., Vol. 96, No. 408, pp. 247–256, doi: 10.1002/qj.49709640807, April 1970. 4. Thurai, M.; Huang, G.J.; Bringi, V.N.; et al.: “Drop Shapes, Model Comparisons, and Calculations of Polarimetric Radar Parameters in Rain,” J. Atmos. Oceanic Technol., Vol. 24, No. 6, pp. 1019–1032, https://doi.org/10.1175/JTECH2051.1, June 2007. 5. Gunn, R.; and Kinzer, G.D.: “The Terminal Velocity of Fall for Water Droplets in Stagnant Air,” J. Meteorol., Vol. 6, No. 4, pp. 243–248, <https://doi.org/10.1175/1520- 0469(1949)006<0243:TTVOFF>2.0.CO;2>, August 1949. 6. Atlas, D.; Srivastava, R.C.; and Sekhon, R.S.: “Doppler radar characteristics of precipitation at vertical incidence,” Rev. Geophys., Vol. 11, No. 1, p. 1, doi: 10.1029/RG011i001p00001, February 1973. 7. Foote, G.B.; and Du Toit, P.S.: “Terminal Velocity of Raindrops Aloft,” J. Appl. Meteorol., Vol. 8, No. 2, pp. 249–253, <https://doi.org/10.1175/1520-0450(1969)008<0249:TVORA>2.0. CO;2>, April 1969. 8. Hou, A.Y.; Kakar, R.K.; Neeck, S.; et al.: “The Global Precipitation Measurement Mission,” Bull. Am. Meteorol. Soc., Vol. 95, No. 5, pp. 701–722, <https://doi.org/10.1175/BAMS- D-13-00164.1>, May 2014. 9. Schönhuber, M.; Lammer, G.; and Randeu, W.L.: “The 2D-Video-Distrometer,” in Precipitation: Advances in Measurement, Estimation and Prediction, S. Michaelides (ed.), Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 3–31, doi: 10.1007/978-3-540-77655-0_1, January 2008. 10. Thurai, M.; Bringi, V.N.; Carey, L.D.; et al.: “Estimating the Accuracy of Polarimetric Radar- Based Retrievals of Drop-Size Distribution Parameters and Rain Rate: An Application of Error Variance Separation Using Radar-Derived Spatial Correlations,” J. Hydrometeorol., Vol. 13, No. 3, pp. 1066–1079, June 2012. 13

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1. Tokay, A.; Petersen, W.A.; Gatlin, P.; and Wingo, M.: “Comparison of Raindrop Size Distribution Measurements by Collocated Disdrometers,” J. Atmos. Oceanic Technol., Vol. 30, No. 8, pp. 1672–1690, https://doi.org/10.1175/JTECH-D-12-00163.1, August 2013. 12. Wen, L.; Zhao, K.; Zhang, G.; et al.: “Impacts of Instrument Limitations on Estimated Raindrop Size Distribution, Radar Parameters, and Model Microphysics during Mei-Yu Season in East China,” J. Atmos. Oceanic Technol., Vol. 34, No. 5, pp. 1021–1037, <https://doi.org/10.1175/ JTECH-D-16-0225.1>, May 2017. 13. Chen, D.; and Chen, H.W.: “Using the Köppen classification to quantify climate variation and change: An example for 1901–2010,” Environ. Dev., Vol. 6, pp. 69–79, <https://doi.org/10.1016/j. envdev.2013.03.007>, April 2013. 14. Skofronick-Jackson, G.; Peterson, W.A.; Berg, W.; et al.: “The Global Precipitation Measurement (GPM) Mission for Science and Society,” Bull. Am. Meteorol. Soc., Vol. 98, No. 8, pp. 1679–1695, https://doi.org/10.1175/BAMS-D-15-00306.1, August 2017. 15. Kruger, A.; and Krajewski, W.F.: “Two-Dimensional Video Disdrometer: A Description,” J. Atmos. Oceanic Technol., Vol. 19, No. 5, pp. 602–617, <https://doi.org/10.1175/1520-0426 (2002)019<0602:TDVDAD>2.0.CO;2>, May 2002. 16. Marshall, J.S.; and Palmer, W.M.K.: “The distribution of raindrops with size,” J. Meteorol., Vol. 5, No. 4, pp. 165–166, <https://doi.org/10.1175/1520-0469(1948)005<0165:TDORWS>2.0. CO;2>, August 1948. 17. Ulbrich, C.W.: “Natural Variations in the Analytical Form of the Raindrop Size Distribution,” J. Clim. Appl. Meteorol., Vol. 22, No. 10, pp. 1764–1775, <https://doi.org/10.1175/1520- 0450(1983)022<1764:NVITAF>2.0.CO;2>, October 1983. 18. Feingold, G.; and Levin, Z.: “The Lognormal Fit to Raindrop Spectra from Frontal Convective Clouds in Israel,” J. Clim. Appl. Meteorol., Vol. 25, No. 10, pp. 1346–1363, <https://doi. org/10.1175/1520-0450(1986)025<1346:TLFTRS>2.0.CO;2>, October 1986. 19. Bringi, V.N.; Chandrasekar, V.; Hubbert, J.; et al.: “Raindrop Size Distribution in Different Climatic Regimes from Disdrometer and Dual-Polarized Radar Analysis,” J. Atmos. Sci., Vol. 60, No. 2, pp. 354–365, <https://doi.org/10.1175/1520-0469(2003)060<0354:RSDIDC>2.0. CO;2>, January 2003. 20. Cao, Q.; Zhang, G.; Brandes, E.; et al.: “Analysis of Video Disdrometer and Polarimetric Radar Data to Characterize Rain Microphysics in Oklahoma,” J. Appl. Meteorol. Climatol., Vol. 47, No. 8, pp. 2238–2255, https://doi.org/10.1175/2008JAMC1732.1, August 2008. 21. Marzuki, M.; Randeu, W.L.; Kozu, T.; et al.: “Raindrop axis ratios, fall velocities and size distribution over Sumatra from 2D-Video Disdrometer measurement,” Atmos. Res., Vol. 119, pp. 23–37, https://doi.org/10.1016/j.atmosres.2011.08.006, January 2013. 14

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1. Testud, J.; Oury, S.; Black, R.A.; et al.: “The Concept of ‘Normalized’ Distribution to Describe Raindrop Spectra: A Tool for Cloud Physics and Cloud Remote Sensing,” J. Appl. Meteorol., Vol. 40, No. 6, pp. 1118–1140, <https://doi.org/10.1175/1520-0450(2001)040<1118:TCO NDT>2.0.CO;2>, June 2001. 23. Douglas, C.A.; and Booker, R.L.: “Visual Range: Concepts, Instrumental Determination, and Aviation Applications,” National Bureau of Standards, NBS Monograph 159, p. 362, 1977. 24. Atlas, D.: “Optical Extinction By Rainfall,” J. Meteorol., Vol. 10, No. 6, pp. 486–488, <https://doi.org/10.1175/1520-0469(1953)010<0486:OEBR>2.0.CO;2>, December 1953. 25. Federal Coordinator For Meteorological Services and Supporting Research, Federal Meteorological Handbook No. 1: Surface Weather Observations and Reports, FCHM-H1-2005, Washington, DC, U.S. Department of Commerce/National Oceanic and Atmospheric Administration, September 2005. 26. Everitt, B.S.; Landau, S.; and Leese, M.: Cluster Analysis, 5th Edition, W.A. Shewhart and S.S. Wilks (eds.), Wiley InterScience, John Wiley & Sons, Ltd., doi: 10.1002/9780470977811, 2011. 15

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REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operation and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To) 01–03–2018 Technical Memorandum 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER 5b. GRANT NUMBER A Rain Taxonomy for Degraded Visual Environment Mitigation 6. AUTHOR(S) P.N. Gatlin and W.A. Petersen 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) George C. Marshall Space Flight Center Huntsville, AL 35812 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) National Aeronautics and Space Administration Washington, DC 20546–0001 12. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified-Unlimited Subject Category 43 5c. PROGRAM ELEMENT NUMBER 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 8. PERFORMING ORGANIZATION REPORT NUMBER M–1458 10. SPONSORING/MONITOR’S ACRONYM(S) NASA 11. SPONSORING/MONITORING REPORT NUMBER NASA/TM—2018–219882 Availability: NASA STI Information Desk (757–864–9658) 13. SUPPLEMENTARY NOTES Prepared by the Science and Technology Directorate, Science Mission Directorate 14. ABSTRACT This Technical Memorandum (TM) provides a description of a rainfall taxonomy that defines the detailed characteristics of naturally occurring rainfall. The taxonomy is based on raindrop size measurements collected around the globe and encompasses several different climate types. Included in this TM is a description of these rainfall observations, an explanation of methods used to process those data, and resultant metrics comprising the rain taxonomy database. Each of the categories in the rain taxonomy are characterized by a unique set of raindrop sizes that can be used in simulations of electromagnetic wave propagation through a rain medium. 15. SUBJECT TERMS precipitation, aviation, meteorology 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF 19a. NAME OF RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE U U U UU 16 PAGES STI Help Desk at email: help@sti.nasa.gov 30 19b. TELEPHONE NUMBER (Include area code) STI Help Desk at: 757–864–9658 Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39-18

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National Aeronautics and Space Administration IS02 George C. Marshall Space Flight Center Huntsville, Alabama 35812