A central element of the debate surrounding the recent decision by South Korea to allow the United States to deploy a Terminal High Altitude Area Defense (THAAD) missile defense system on its territory is the range of the THAAD’s radar. China argues that the THAAD radar will be able to look deep into its territory; supporters of the deployment counter that the radar will be configured so that its range will be limited.
The radar used with a THAAD battery is the X-band AN/TPY-2. The TPY-2 radar has two configurations. It can be configured as Terminal Mode (TM) radar, in which it operates as the fire control radar for a THAAD battery. Alternatively, it can be set up as a Forward-Based Mode (FBM) radar, in which it relays tracking and discrimination data to a remote missile defense system, such as the U.S. Ground-Based Midcourse (GMD) system. If THAAD is deployed to South Korea, The United States has stated that its TPY-2 radar would be in the shorter-range TM configuration. Since in the TM mode, the radar reportedly only has a range of 600 km, supporters of the THAAD deployment argue that while its range is adequate to cover N. Korea, it cannot look deeply into China. Critics of this argument point out that in the FBM mode the radar has a much greater range, and that the radar can be converted from TM to FBM (or vice versa) in only eight hours or less. According to a U.S. Army manual, “The hardware used by the two modes is identical, but their controlling software, operating logic, and communications package are different.” In addition the radar is highly mobile: it can be transported by air and can be operational with four hours of reaching its deployment site.
Published figures for the range of a TPY-2 radar vary by nearly a factor of five. For a radar, this is a huge discrepancy. If all these published ranges were for the same target and same radar operating parameters, they would indicate a difference in radar capability of about 54 = 625. So clearly these claims must reflect very different assumptions about how the radar is used.
To provide a sense of how the range is affected by how the radar is operated, I will step through various claims about the TPY-2’s range, from lowest to highest. Comparing these claims is complicated by the fact that many of them are not accompanied by much information on the conditions under which the range is achieved. Nevertheless, the comparison shows that the widely varying ranges are self-consistent once differences in how the radar is operated and the nature of the target are taken into account. At the same time, it also shows how claims about the radar’s range can be misleading if applied in the wrong context.
(1) Several hundred miles. The shortest range claim I have seen is from the TPY-2’s manufacturer, the Raytheon Company, and is that a TPY-2 radar could “…track a home run from a ball park from several hundred miles away.” If we take several hundred to mean three hundred, then this range is about 480 km. [The home run would have to be hit very high – over 44,000 feet [altitude corrected per reader comment below] – to rise over the horizon at this range.] A reflective sphere the size of a baseball (diameter = 2.9 inches) has a radar cross section (RCS) of about 0.004 m2. While this RCS certainly possible, it is lower than is usually used for a baseline number. If we scale to a radar cross section of 0.01 m2, we get a range of about 600 km. This range is consistent with the terminal mode range cited in South Korean press reports.
(2) 600 km. This is the range cited in South Korean press reports for the range of the TPY-2 in the terminal mode. In February 2015, the Chosun Ilbo cited a government official as saying the TM configuration had an effective range of 600 km. In April 2015, the Seoul Shinmum (in Korean) gave this range for the TM radar, citing a U.S. technical report.
(3) 870 km. This is the range estimate given in a post in this blog from September 21, 2012 (by George Lewis and Theodore Postol). I will use this post as the baseline for the discussion because it contains values for of all the parameters used in the radar range calculation. The link is: https://mostlymissiledefense.com/2012/09/21/ballistic-missile-defense-radar-range-calculations-for-the-antpy-2-x-band-and-nas-proposed-gbx-radars-september-21-2012/#more-420.
(4) 1,500 km. A figure in the 2013 National Academy of Sciences (NAS) report show a tracking range curve with radii of about 1,500 km for the TPY-2 radar. The NAS panel has stated that this 1,500 km range is conservative.
(5) Greater than 1,732 km. The NAS panel says a range of 1,732 km would be obtained using the Lewis and Postol parameters in point (3) except with the required S/N reduced from 20 to 12.4 and the dwell time increased from 0.1 s to 1.0 s. They further say that if the actual classified values of the other parameters were used instead of the values in (3), the range would be even greater.
(6) 1,800-2,000 km. The ranges given in the South Korean Press for the forward-based configuration of the TPY-2 radar (same sources as in item (2) above).
(7) Greater than 2,900 km. In 2008, Major General Patrick O’Reilly (then the Deputy Director of the MDA) stated that the TPY-2 had a range “greater than 1,800 miles” (1,800 miles = 2,900 km).
(8) 3,000 km. This range is shown in a figure published in the South Korean newspaper, based on a calculation by George Lewis and Theodore Postol. The figure is reproduced as Figure 1 below.
Figure 1. TPY-2 tracking geometries for a radar in South Korea for a launch point in China.
How is such a wide span of ranges possible? Because of different assumptions regarding the operating mode of the radar and the nature of the target.
Start with the 870 km range in point (3) as a baseline. The key assumptions and parameters here are: a warhead target with a radar cross section (RCS) of 0.01 square meters; a radar dwell time (the amount of time the radar spends on each beam position) for each target of 0.1 seconds; and a signal to noise (S/N) ratio for detection of S/N = 20. This result indicates that the radar could track 10 incoming targets at a range of 870 km making one measurement on each target every second, or alternatively 100 targets with a measurement every ten seconds. The assumption of 0.1 second for the dwell time is somewhat arbitrary and does not necessarily match what is used in the actual TM and FBM configurations (which is classified).
Now consider the ranges in points (1) and (2) above. These clearly correlate to the terminal mode configuration of the radar, with a nominal range of 600 km. Is this short-range range reasonable? In the terminal mode, the targets will be either individual warheads or entire missiles descending toward their impact points (although in some cases, targets might be detected before they reach the peak of their trajectories). Unless the targets are tumbling, then they will generally be viewed in close to a nose-on geometry, so that their RCS will likely be relatively low. Thus the 0.01 square meter RCS assumed in the baseline seems appropriate, although it could be lower. In this mode, operating as a fire control radar for a THAAD battery, the radar might have to deal with dozens or even a hundred or more simultaneous targets. In addition the radar will also be required to carry out continuous surveillance (search) for new targets. Thus it would not be surprising that the range in this mode would be less than the estimate in (3), and 600 km seems plausible.
Now let’s look at the 1,500 and 1,732+ km ranges drawn from the NAS report in points (4) and (5). The radar and target parameters used in the NAS report are classified. However, from the discussion of point (5), it is apparent that most of the difference in range relative to the 870 km range in point (3) is due to a longer dwell time – in the case of the 1,732+ range a factor of ten increase in dwell time per target – which gives as factor of 1.78 times increase in range. That is, the increase in range is obtained at the price of a ten-fold decrease in the number of targets that can be tracked or a ten-fold increase in the time between measurements on each target (or some combination of the two). As with (3), these ranges do not take into account a requirement for the the radar to conduct surveillance for new targets (for example, if the radar was receiving precise cues to new targets from other sensors so that surveillance was not necessary).
This longer dwell time per target might be similar to what the TPY-2 radar uses in its forward-based mode to get the 1,800-2,000 in point (6) above. In the forward-based mode, the radar is primarily focused on tracking smaller numbers of longer-range missile early in their flights and at longer ranges. However, it seems likely that in the FBM mode the radar also has surveillance requirements, which would suggest a shorter range. On the other hand, the description of the FBM configuration radar by both the MDA and its manufacturer emphasize that it is intended to track missiles during their boost phase. At the TPY-2’s X-band frequency (approximately 10 GHz), the upper stages of ballistic missiles would be expected to have much larger radar cross sections than separated warheads. For example, the 2003 American Physical Society Boost Phase Study used a radar cross section of 0.094 square meters for a solid-fuel missile as it rises over the horizon of a TPY-2 radar (and 0.45 square meters for a liquid-fuel missile).  If such large radar cross sections are assumed (9.4 to 45 times larger than the 0.01 square meters assumed in point (3) for a warhead), ranges of 1,800 to 2,000 km could be achieved with dwell times less than those in used for the NAS’s ranges in points (4) and (5) even if the radar devoted half of its time to surveillance.
Finally, if one combines a boost phase tracking assumption (target radar cross section = 0.1 square meters) with longer dwell times (0.1 s) and no surveillance requirement, ranges as great as the 2,900+ km cited by General O’Reilly in (7) or the 3,000 km figure from Lewis and Postol in (8) are obtained.
The above discussion shows that while the United States’ argument that THAAD’s range while operating in its intended terminal mode is very limited is plausible, so is the Chinese claim that the radar is physically capable of observing missile flights deep within its territory. While China would surely be able to monitor which mode the radar is operating in, there does not appear to be any technical or legal barrier to prevent it from being quickly converted from terminal to forward-based mode.
 Quotation from: Park Hyun, “Pentagon Document Confirms THAAD’s Eight-Hour Conversion Time,” June 3, 2015. Available at: http://english.hani.co.kr/arti/english_edition/e_international/694082.html.
 Raytheon Company, “Sharp Eyes for Missile Defense – Bus-size Radar Rolls Like a Truck, Sees Like a Hawk,” August 26, 2015, Available at: http://www.raytheon.com/news/feature/an_tpy2_radar_behind_headlines.html.
 “U.S. Seeks Compromise Over Missile Defense System,” The Chosun Ilbo (English Edition), February 24, 2015. Available at: http://english.chosun.com/site/data/html_dir/2015/02/24/2015022400979.html.
 Cited in: “News Analysis: U.S. Defense Chief’s Visit to Seoul Adds Controversy to THAAD Deployment,” China.org.cn, April 9, 2015.
 National Research Council, Making Sense of Ballistic Missile Defense: An Assessment of Concepts and System for U.S. Boost Phase Missile Defense in Comparison to Other Alternatives (Washington, D.C.: National Academies Press, 2012), p. 115. Available at: http://www.nap.edu/catalog.php?record_id=13189.
 Letter sent to Congress by Members of NAS Panel, “Setting the Record Straight – NRC Study Entitled “Making Sense of Ballistic Missile Defense,”” January 11, 2013 (including David Barton, “Attachment 1 – A Brief Rebuttal to Lewis and Postol Radar Claims,” (dated December 31, 2012)).
 NAS Panel, “Setting the Record Straight.”
 Park Hyun, “An/TPY-2 Radar Could Track any Chinese ICBMs as They Pass Over the Korean Peninsula,” The Hank Yoreh (English Edition), June 2, 2015. Available at: http://english.hani.co.kr/arti/english_edition/e_international/693916.html.
 The other parameters are radar average power = 81,000 W, antenna aperture = 9.2 square meters, antenna gain = 103,000, radar system temperature = 400 K, radar system losses = 6.3.
 This also assumes a different beam position is needed for each target.
 Report of the American Physical Society Study Group on Boost-Phase Intercept Systems for National Missile Defense, July 2003, Vol. 2., p. 177. Available at: http://journals.aps.org/rmp/pdf/10.1103/RevModPhys.76.S1.