A Proposed Low Distortion Projection for the City of Las Cruces and Dona Ana County Scott Farnham, PE, PS City Surveyor, City of Las Cruces NM October 2020 Introduction As part of the ongoing modernization of the U.S. National Spatial Reference System (NSRS), the National Geodetic Survey (NGS) will replace our horizontal and vertical datums (NAD83 and NAVD88) with new geometric datums assigned in the North American Terrestrial Reference Frame of 2022 (NATRF2022). The City of Las Cruces / Dona Ana County and the City of Albuquerque / Bernalillo County submitted proposals to NGS to incorporate Low Distortion Projections (LDP) as part of the New Mexico State Plane Coordinate Systems. Approval by NGS was obtained on June 17, 2019 for the proposed systems (see approval notice). Design of the LDP is the responsibility of the submitting agencies and must be submitted to NGS on or prior to March 31, 2021. Mark Marrujo1 with NMDOT is submitting final LDP design forms to NGS for the State of New Mexico. The City of Las Cruces (City) is designing a new Low Distortion Projection for Public Works Department, Engineering and Architecture projects to NGS criteria. To meet NGS LDP minimum size and shape criterion, the LDP area extends to Dona Ana County (County) boundary lines. This report presents design analysis and conclusions of the proposed City / County local NGS LDP system for stakeholders’ review prior to NGS final design submittal. NGS NM SPCS2022 Zones and Stakeholder Organizations NGS is designing new State Plane Coordinate Systems (SPCS2022) for New Mexico. The default SPCS2022 designs for the State are a statewide single zone and the three State Plane Zones: West, Central, and East. The two local LDP zones proposed are part of Layer 3 of the SPCS2022 zones. The submitted NGS SPCS2022 Zone Request and Proposal Form for New Mexico proposed Layer 3 LDP zones lists the following stakeholder organization representatives. NGS requires all stakeholders are supportive of the LDP designs for the March 31st submittal. 1. New Mexico Department of Transportation 2. New Mexico Professional Surveyors 3. New Mexico Board of Licensure for Professional Engineers & Professional Surveyors 4. New Mexico Department of Information Technology – GAC 5. City of Las Cruces 6. Dona Ana County 7. City of Albuquerque 8. Bernalillo County Letters of Support to NGS, William (Bill) Stone2, were provided from: ➢ New Mexico Professional Surveyor’s (NMPS) ➢ New Mexico Department of Transportation (NMDOT) 1 Mark Marrujo, PS: Survey & Lands Engineering Manager, NM Department of Transportation 2 Bill Stone: SW Region (NM, UT, AZ) Geodetic Advisor, NOAA’s NGS 1 A Proposed Low Distortion Projection for the City of Las Cruces and Dona Ana County LDP Objective The objective for a local Low Distortion Projection Coordinate System is to reduce linear distortion at the topographic surface such that it is negligible for most practical applications. The motivation for a local Low Distortion Projection is to have a consistent set of projected coordinates that yield distances so close to horizontal ground distances that no additional scale factor is required. Many statewide and LDP systems have been officially adopted by states and local governments: • Wisconsin • Minnesota • Oregon • Kansas • Indiana • Navajo Nation (NM, AZ, UT, CO) Source: SP_NOS_NGS_13.pdf 1 Examples of U.S. LDP Coordinate Systems The City / County LDP design objective is based on NGS criteria used in development of the state’s default zones and is tied to linear distortion, population densities, and municipal areas. ❖ A minimum linear distortion that satisfies all three of the following minimum percentages: o 50% of total zone area o 75% of cities and towns, irrespective of population o 90% of zone population For the City / County, a goal of ±25 ppm or less was selected ➔ 1:40,000 or 0.132 ft per mile (0.025 ft per 1,000 ft). The City of Las Cruces LDP criterion is a linear distortion of ±15 ppm or less ➔ 1:66,667 or 0.079 ft per mile (0.015 ft per 1,000 ft). A minimum zone size designed by stakeholders needs to meet the following requirements. ❖ Create the largest zone possible, meeting distortion design criterion, to avoid creating an excessive number of small SPCS2022 zones within a state. ❖ Minimum zone width is 50 km (31 miles) for a zone with topographic height range of 250 m (820 ft) or less. For reference, linear distortion changes at a rate of 15.7 ppm per 100 m change in topographic height (4.8 ppm per 100 ft). It decreases (becomes more negative) with increasing height, and vice versa. The reader is referred to Procedures for Design and Modification of the State Plane Coordinate System of 2022 for in-depth criteria review. 2 A Proposed Low Distortion Projection for the City of Las Cruces and Dona Ana County U.S. Survey Foot vs International Foot New Mexico uses the U.S. survey foot definition, 1 foot = 1200/3937. NGS will deprecate the U.S. survey foot with a planned effective date of December 31, 2022 and is independent of the National Spatial Reference System (NSRS) modernization timeline. We expect New Mexico legislation will eventually change the foot definition to the international foot. The City / County LDP coordinate system uses the International foot definition: ❖ 1 foot = 0.3048 meter exactly See the NIST U.S. survey foot site for more details. Zone Name The City / County LDP design parameters were set on November 5, 2019. Until final NGS approval, and to allow for potential design changes, the City / County LDP reference name is: CLC_5NOV19. Final submittal zone parameters and test values required on the NGS SPCS2022 Zone Design Submittal Form (Items 9 & 10) will be referenced with the prefix NM_DAC_SPCS2022_Layer3. Final zone names are determined by NGS. Design Parameters The City / County zone defining parameters must meet NGS criteria, that include: ➢ The zone origin (Latitude/Longitude) and projection axis scale must be unique for all SPCS2022 zones. ➢ Latitude/Longitude be evenly divisible by 3 to avoid infinitely repeating digits. ➢ The projection axis scale defined to 6 decimal places. ➢ Projection grid origins (false northings and eastings) defined in meters with whole numbers evenly divisible by 1,000 meters such that all zone coordinates are positive. ➢ False northing is exactly zero. The City / County LDP design was evaluated using the Transverse Mercator projection (TM) that delivers high accuracy in zones less than a few degrees in east-west extent (current New Mexico State Plane Projection is a TM projection). The zone origin Longitude was evaluated to best balance population density along the Rio Grande valley and passes close to City of Las Cruces geographic center. Zone coordinates (meters) range from 12,500N/16,100E at the southwest corner to 474,000N/311,400E at the zone northeast corner. 3 A Proposed Low Distortion Projection for the City of Las Cruces and Dona Ana County Table 1 provides final CLC_5NOV19 LDP parameters. Table 1 CLC_5NOV19 – A Low Distortion Projection for City of Las Cruces & Dona Ana County UNITS Metric / iFT (International Feet) Horizontal Datum NAD83 (2011) epoch 2010.0 (Local Geographic System: EPSG 6318) GRS80 Ellipsoid: EPSG 7019 Semi-Major Axis 6378137 meter exact Inverse Flattening 298.257222101 unity (12 significant digits min.) . Vertical Datum NAVD88 Projection Transverse Mercator (Gauss-Kruger form) GEOID GEOID 18: NGS latest hybrid geoid model, intended to be used with NAD83 (2011) epoch 2010.00. Geoid 18 provides orthometric heights consistent with NAVD 88. See NOAA Technical report NOS NGS 72 for more detail. Projection Origin Latitude N31°45’00.0” 31.75° Longitude W106°48’00.0” -106.80° (253.20°) False Northing 0.0000 False Easting 52,000.0000 m 170603.675 iFT Scale 1.000195 exact height: 1240 m (4068.2) . NGS is not expected to release the NATRF2022 datum and geoid until 2024/2025 timeline. NGS uses ITRF2014 / ITRF2020 in their modeling effort and there are interim in-progress xGEOID models available from the NGS web site. See NGS site BETA and Delayed Release of the Modernized NSRS for more information. NGS Data Release NGS has provided preliminary New Mexico SPCS2022 design and zone linear distortion maps, design Excel spread sheets, and ESRI Shape files for the New Mexico default zones. The shape file and spread sheets provide 1 km ellipsoid height grid points (ITRF2014) and population densities from the 2010 U.S. Census data. The NGS Excel spread sheet, provided by Michael Dennis3, was modified to be specific to the Dona Ana County zone limits. The spreadsheet includes design calculations and statistical reporting from data that includes ITRF2014 1km grid data: ellipsoid heights, grid scale factors, distortion ppm, geometric mean curve radius, latitude and longitude, population grid points, City points and populations. The spreadsheet is complex and may be opened here for review: DAC- CLC_TB_DesignEqArea_ITRF2014. 3 Michael L. Dennis, Ph.D., P.E., R.L.S., M.ASCE: NGS SPCS2022 Project Manager 4 A Proposed Low Distortion Projection for the City of Las Cruces and Dona Ana County Preliminary SPCS2022 Design Maps and Map Data may be downloaded from the NGS site. For New Mexico, the following maps are available and may be viewed with the following links. ➢ Existing SPCS 83 Central Zone Design: 0% population, 0% cities and towns, 0% zone area meet NGS criteria of +/-100 ppm (1:10,000 = +/-0.53 ft per mile). ➢ Preliminary SPCS2022 Default Central Zone: 92% population, 81% cities and towns, 72% zone area meet NGS criteria of +/-100 ppm (1:10,000 = +/-0.53 ft per mile). ➢ Existing UTM Zone 13 North (Used as a statewide zone): 73% population, 48% cities and towns, 50% zone area meet NGS criteria of +/-500 ppm (1:2,000 = +/-2.64 ft per mile).