
    LEE’S SUMMIT, MISSOURI and Raytown, Missouri, Petitioners, v. SURFACE TRANSPORTATION BOARD and United States of America, Respondents. Missouri Central Railroad Company, Intervenor.
    No. 99-1435.
    United States Court of Appeals, District of Columbia Circuit.
    Argued Sept. 7, 2000.
    Decided Nov. 14, 2000.
    Steven J. Kalish argued the cause and filed the briefs for petitioners.
    Evelyn G. Kitay, Attorney, Surface Transportation Board, argued the cause for respondents. With her on the brief were Ellen D. Hanson, General Counsel, and M. Alice Thurston, Attorney, U.S. Department of Justice. Evelyn S. Ying, Attorney, entered an appearance.
    
      Stuart F. Pierson and David C. Reeves were on the brief for intervenor.
    Daniel A. LaKemper was on the joint brief of amici curiae Keokuk Junction Railway Co. and Arkansas-Oklahoma Railroad, Inc.
    Before: GINSBURG, RANDOLPH, and TATEL, Circuit Judges.
   Opinion for the Court filed by Circuit Judge RANDOLPH.

RANDOLPH, Circuit Judge:

This is a joint petition for review of orders of the Surface Transportation Board authorizing the restoration of service over, and trackage rights to operate on, an existing but unused 278 mile railroad line in Missouri. Petitioners, the cities of Lee’s Summit and Raytown, contend that the Board erred in deciding that its regulations required no environmental review under the National Environmental Policy Act (NEPA), 42 U.S.C. § 4321, et seq.

I.

In December of 1997, GRC Holdings Corporation filed a notice with the Board to acquire from the Union Pacific Railroad Company a railroad line and associated real property. The line runs from the eastern border of Missouri to the city of Pleasant Hill near the western border of the state. GRC announced its intention to retain the real property not needed for rail operations and to convey the line to the Missouri Central Railroad Company. Missouri Central filed a Notice of Exemption, indicating that it intended to acquire the line from GRC, and to obtain trackage rights from Union Pacific to operate over additional segments at the line’s eastern and western ends. GRC and Missouri Central sought to avoid full Board review of the transaction, claiming an exemption under 49 U.S.C. § 10502.

The cities of Lee’s Summit and Raytown are located on the 24.8 mile segment at the western end, with respect to which Missouri Central proposed obtaining trackage rights from Union Pacific. The cities petitioned the Board to reject GRC’s and Missouri Central’s claim for exemption. Of the arguments the cities raised, only one is before us — namely, that the Board’s regulations obligated it to perform an environmental assessment of the transaction.

The regulations require such an assessment when the acquisition of a segment of rail or the construction of track results in “either ... an increase in rail traffic of at least 100 percent (measured in gross ton miles annually) or an increase of at least eight trains a day on any segment of rail line affected by the proposal.” 49 C.F.R. § 1105.7(e)(5)(i)(A). An environmental assessment is also required when an acquisition results in “[a]n increase in railyard activity of at least 100 percent (measured by carload activity).” 49 C.F.R. § 1105.7(e)(5)(i)(B).

Much of the Missouri line had not been used since 1979, although it had never been formally abandoned. The cities argued that the increase in rail traffic from the present level of zero to the levels proposed by the transaction — two trains a day five days per week — constituted at least a 100 percent increase in gross annual tons and therefore compelled an environmental assessment. The Board denied the cities’ petition. Missouri Central Railroad Company-Acquisition and Operation Exemption-Lines of the Union Pacific Railroad Company, S.B. Finance Docket No. 33508; GRC Holdings Corporation-Acquisition Exemption-Union Pacific Railroad Company, STB Finance Docket No. 33537 at 6 (STB served Apr. 30, 1998) (“1998 Decision”). As the Board saw it, when “a line currently carries no traffic, any resumption of service, no matter how small, represents an increase mathematically of infinite magnitude.” Id. at 7. The Board therefore turned to the alternative measurement of eight trains per day, drawing an analogy to transactions in which carriers reinstate service on abandoned lines. For abandoned lines an environmental assessment is required only when the restored operations amount to eight trains per day. Id. (citing 49 C.F.R. § 1105.7(e)(5)(i)(C)). Thus, “reading the regulations as a whole,” the Board declined to order an assessment.

On their petition for reconsideration, the cities offered an additional argument: Missouri Central’s planned rail car interchange at Pleasant Hill, at the beginning of the western “trackage rights” segment, required an environmental assessment because the facility constituted a “rail yard” and the activity there would increase at least 100 percent. Without deciding whether the Pleasant Hill facility constituted a “rail yard,” the Board ruled again that it would be “inappropriate to apply a percentage increase to a base of zero.”

II.

When there is doubt about a party’s constitutional standing, the court must resolve the doubt, sua sponte if need be. See Steel Co. v. Citizens for a Better Environment, 523 U.S. 83, 118 S.Ct. 1003, 140 L.Ed.2d 210 (1998); National Ass’n of Reversionary Property Owners v. Surface Transp. Bd., 158 F.3d 135, 141 n. 12 (D.C.Cir.1998). Here the cities’ Article III standing is unclear because, under the Board’s regulation (49 C.F.R. § 1105.6(c)(4)), the acquisition of trackage rights can never trigger a mandatory environmental assessment, and yet the cities are located on the western “trackage” portion of the line. This suggests that the cities were not injured or perhaps could not get redress. If the Board had ordered an environmental evaluation, one might assume that it would have dealt only with the portion of the line to the east of the cities; hence the effect of the increased rail traffic in the cities’ vicinity would not have been evaluated in any event. Oral argument brought some new information to light. We learned from Board counsel that if an environmental assessment is required for one portion of a line, the Board’s practice is to conduct the assessment for the entire transaction, which in this case would include the line running near the cities. For this reason we are satisfied that the cities have demonstrated the requisite “injury in fact” “fairly traceable” to the Board that can be “redressed by a favorable decision.” Lujan v. Defenders of Wildlife, 504 U.S. 555, 560-61, 112 S.Ct. 2130, 119 L.Ed.2d 351 (1992). The Board, we should add, agrees that the cities have standing.

III.

On the merits, the main issue is whether the Board improperly disregarded the part of its regulation demanding an environmental assessment whenever the acquisition of rail line would result in “an increase in rail traffic of at least 100 percent (measured in gross ton miles annually).” 49 C.F.R. § 1105.7(e)(5)(i)(A). The cities believe that an increase from zero tonnage to whatever gross tonnage is represented by 520 trains per year (10 per week) equals an “increase in rail traffic of at least 100 percent.” How the cities calculate this is a mystery. The regulation asks the question: what is the percentage increase on the acquired line? Suppose there were 100 tons per year before the acquisition and 200 tons afterwards. One does not have to be a Richard Feynman to figure out that 200 tons is 100% greater than 100 tons. The formula 100 x (a -f- b) yields the percentage, when a equals the post-acquisition increase in tonnage (100 tons) and b equals the pre-acquisition tonnage (100 tons). But there is trouble when b equals zero, as it does here. Then there must be division by zero. Yet as mathematicians know, “you can’t legitimately divide by 0. ^ doesn’t mean anything.” ROBERT KAPLAN, THE NOTHING THAT Is 73 (1999); see also Charles Seife, Zero 23 (2000) (“[djividing by zero destroys the entire framework of mathematics”).

We may approach the problem differently by trying to calculate what percentage the post-acquisition traffic represents of the pre-acquisition traffic. Suppose 1 train equals 1 ton. The Missouri Central will run 10 trains per week on the line, 52 weeks per year. What percentage of zero tons is 520 tons? Once again, as a matter of mathematics, the answer is problematic. If one asked what is 5% of 100, multiplying .05 x 100 yields 5. But if we ask what is 5% of 0, the answer is 0. Zero multiplied by any number is zero. So what is 100% of 0? Zero of course. One might say, and this perhaps is what the cities have in mind, that since zero is 100% of zero, it follows that anything (any tonnage) greater than zero must trigger the assessment. But the Board had an additional good reason for not reading its regulation this way. Another subsection of the regulation — 49 C.F.R. § 1105.7(e)(5)(i)(C) — provides that “[flor a proposal ... to construct a new line or re-institute service over a previously abandoned line, only the eight train a day provision ... will apply.” All abandoned lines will, by definition, have had zero traffic. The Board thought that the Missouri Central line was analogous; it had been without traffic for nearly 20 years. 1998 Decision at 7; Missouri Central Railroad Company—Acquisition and Operation Exemption—Lines of Union Pacific Railroad Company, STB Finance Docket No. 33508; GRC Holdings Corporation—An Acquisition Exemption—Union Pacific Railroad Company, STB Finance Docket No. 33537 at 2 (STB served Sept. 14, 1999). Although the Board refused to find a “de facto” abandonment here, it did not have to ignore its abandonment rule. If the cities’ argument were credited, any increase in traffic above zero would trigger an assessment; yet in the comparable situation of an abandoned line being reactivated, an assessment would be triggered only if the new traffic amounted to eight trains per day. To maintain some consistency in its regulatory treatment of these closely analogous situations, the Board therefore decided to apply the eight-trains-per-day portion of the rule to this transaction.

It is true that the Board’s resolution is not perfect. If on the same rail line involved in this case, there had been 1 train per day, five days per week (instead of zero traffic), the increased traffic after the acquisition would have required an environmental assessment because 2 trains per day over the same period (assuming equal weight) amounts to a 100% increase. So an environmental assessment would be required for an increase of 1 train per day but not, as here, for an increase of 2 trains per day on the same line. That, say the cities, is senseless.

They have a point but so does the Board when it relies on the manner in which it treats abandoned lines. There is, as we have indicated, no perfect solution to the problems posed by applying the 100% increase standard to a baseline of zero. In these circumstances, the Board’s interpretation of its regulation is deserving of respect. Application of the eight trains per day standard is not “plainly erroneous or inconsistent with the regulation.” United States v. Larionoff, 431 U.S. 864, 872, 97 S.Ct. 2150, 53 L.Ed.2d 48 (1977); Bluestone Energy Design, Inc. v. FERC, 74 F.3d 1288,1292 (D.C.Cir.1996).

The petition for judicial review is denied. 
      
      . The cities do not challenge the validity of the regulations.
     
      
      . For the reasons stated in the text, the Board also properly refused to require an assessment based on the increased activity at the Pleasant Hill exchange. Even if the exchange were a "rail yard,” the Board determined that its 100 percent standard could not be applied because pre-acquisition activity was zero. See 49 C.F.R. § 1105.7(e)(5)(i)(B).
     
      
      . We reject the cities' claim that rehabilitation of the line will constitute construction of track and therefore trigger an assessment under a different regulation (49 C.F.R. § 1105.6(b)(1)). Improvement of existing track does not constitute "construction,” and does not even trigger Board jurisdiction under 49 U.S.C. § 10901. City of Detroit v. Canadian Nat'l Ry., 9 I.C.C. 1208, 1215-17 (1993), aff'd sub nom. Detroit/Wayne County Port Auth. v. ICC, 59 F.3d 1314, 1316-17 (D.C.Cir.1995).
     