
973 A.2d 174 (2009)
FRATERNAL ORDER OF POLICE/DEPARTMENT OF CORRECTIONS LABOR COMMITTEE, Appellant,
v.
DISTRICT OF COLUMBIA PUBLIC EMPLOYEE RELATIONS BOARD, Appellee.
No. 07-CV-1089.
District of Columbia Court of Appeals.
Argued December 16, 2008.
Decided June 11, 2009.
*175 J. Michael Hannon, Washington, for appellant.
Bruce A. Frederickson, with whom Cedar P. Carlton was on the brief, for appellee.
Before REID, GLICKMAN and THOMPSON, Associate Judges.
THOMPSON, Associate Judge:
Appellant, the Fraternal Order of Police/Department of Corrections Labor Committee ("FOP"), acting on behalf of three of its members (the "aggrieved correctional officers" or "the officers"), seeks review of an order of the Superior Court upholding a decision of the District of Columbia Public Employee Relations Board (the "PERB" or the "Board"). In the decision at issue, the PERB modified an arbitrator's award of backpay to the aggrieved officers. Because we conclude that the PERB decision is supported by substantial evidence in the record and reflects an interpretation of the District of Columbia Comprehensive Merit Personnel Act (the "CMPA") that is not plainly erroneous, we affirm.

I.
In August 2000, the District of Columbia Department of Corrections ("DOC") terminated the employment of the aggrieved correctional officers, finding that they had assaulted an inmate. Pursuant to a Memorandum of Agreement, FOP and DOC submitted their dispute over these removals to arbitration. Arbitrator Jerome Barrett held a hearing and issued a written decision dated October 16, 2004, in which he found that the removals were unwarranted and that the officers were entitled to reinstatement. Arbitrator Barrett ordered that the officers "shall receive back pay, with interest, for the period for which *176 each was separated [from his employment], in accordance with the [federal] Back Pay Act."[1] The arbitrator further stated in his order that "in the absence of any citation to authority to allow offset of interim earnings against back pay due," he would not "direct such offset."[2] DOC sought review by the PERB.
The PERB upheld the arbitrator's award in all other respects, but modified the award to correct the arbitrator's refusal to "disallow[ ] offset for interim earnings." The PERB found that this aspect of the arbitral award was "contrary to law because it violates ... the Back Pay Act." The PERB further explained its ruling as follows:
[W]e are not saying that an arbitrator cannot use his/her equitable power to deny a deduction for an offset of earnings; however, where an arbitrator expressly states (as he has in the present case) that he relied on a specific statute for awarding back pay and that statute expressly requires offset of earnings, the arbitrator must follow the statutory mandate.
After the Superior Court affirmed the PERB's decision, FOP timely appealed to this court. We review a decision of the PERB "as if the [appeal from the PERB decision] had been heard initially in this court" rather than in the Superior Court. Gibson v. District of Columbia Pub. Employee Relations Bd., 785 A.2d 1238, 1241 (D.C.2001). The issue before us is whether the PERB committed reversible error in overturning the part of the arbitration decision that prevented the DOC from deducting the aggrieved officers' interim earnings from their back pay award.

II.
This court will not easily disturb a decision of the PERB. Rather, we must defer to the Board's factual findings if they are supported by "substantial evidence," and we defer to the Board's interpretation of the CMPA unless the interpretation is "unreasonable in light of the prevailing law or inconsistent with the statute" or is "plainly erroneous." Doctors Council of the Dist. of Columbia Gen. Hosp. v. District of Columbia Pub. Employee Relations Bd., 914 A.2d 682, 695 (D.C.2007) (citation omitted); Public Employee Relations Bd. v. Washington Teachers Union Local 6, AFT, 556 A.2d 206, 207 (D.C. 1989). Unless "rationally indefensible," a PERB decision must stand. Drivers, Chauffeurs, & Helpers Local Union No. 639 v. District of Columbia, 631 A.2d 1205, 1216 (D.C.1993).
*177 The PERB itself has limited authority to overturn an arbitral award. Pursuant to the CMPA, the PERB may modify, set aside, or remand an arbitration award only under circumstances specified in the statute, including where "the award on its face is contrary to law and public policy." D.C.Code § 1-605.02(6) (2001). "Absent a clear violation of law  one evident on the face" of the arbitrator's award, the PERB lacks "authority to substitute its judgment for the arbitrator's." MPD, supra note 2, 901 A.2d at 789 (internal quotation marks omitted).[3]

III.
FOP contends that the PERB's decision  specifically, the Board's conclusion that the arbitrator's back-pay-without-offset award is "contrary to law"  is "rationally indefensible." The premise of FOP's argument is that "[a]t the time of this award, the relevant and applicable D.C. law did not require arbitrators to offset interim earnings in a back pay award for wrongfully terminated city employees."[4] The PERB did not disagree with FOP's premise about the requirements of District of Columbia law, and, in fact, pointedly explained that it was "not saying that an arbitrator cannot use his/her equitable power to deny a deduction for an offset of earnings."[5] It does not follow, however, that the PERB's characterization of the arbitrator's decision as "contrary to law" was rationally indefensible or plainly erroneous.
As we read the PERB decision, it reflects the Board's interpretation that one circumstance in which an arbitrator's *178 award "on its face is contrary to law and public policy" within the meaning of the CMPA (specifically, D.C.Code § 1-605.02(6)) is where, in arriving at the award, the arbitrator looks to an external law for guidance and purports to apply that law, but overlooks or ignores the law's express provisions. This appears to be the interpretation that underlies the Board's statement that "where an arbitrator expressly states (as he has in the present case) that he relied on a specific statute for awarding back pay and that statute expressly requires offset of earnings, the arbitrator must follow the statutory mandate."
In our view, section 1-605.02(6) does not compel the foregoing interpretation. The statutory phrase "award on its face is contrary to law and public policy" could reasonably be interpreted to mean something else; for example, the phrase could mean what FOP urges, i.e., that an arbitral "award on its face is contrary to law and public policy" only if the award actually is prohibited by relevant and applicable law. However, we are obligated to defer to the PERB's interpretation of the CMPA language unless the interpretation is plainly erroneous, a conclusion we are unable to reach here.[6] As we ourselves have previously reasoned, the statutory reference to an award that "on its face is contrary to law and public policy" may include an award that was premised on "a misinterpretation of law by the arbitrator that was apparent `on its face.'" MPD, supra note 2, 901 A.2d at 787-88 (italics omitted). That is precisely what the PERB found to exist here.
Substantial evidence supports the PERB's finding that the arbitrator "relied on the Back Pay Act" as the basis for awarding relief to the aggrieved officers. In the remedy portion of his decision, Arbitrator Barrett ordered "back pay, with interest, for the period for which each [aggrieved officer] was separated [from his employment], in accordance with the Back Pay Act" (emphasis added). And, in describing DOC's termination of the officers as an "unwarranted personnel action," Arbitrator Barrett used a term of art set forth in the Back Pay Act. See 5 U.S.C. § 5596(b)(1) (2006).[7]
The Back Pay Act permits the award of "all or any part of the pay, allowances or differentials, as applicable which the employee normally would have earned or received during the period if the [unlawful] personnel action had not occurred [i.e., "back pay"], less any amounts earned by the employee through other employment during that period." 5 U.S.C. § 5596(b)(1)(A)(i) (emphasis added). This language is "clear on its face," Doctors Council, supra, 914 A.2d at 697; as FOP admits, it unambiguously requires that back pay awarded to a wrongfully-terminated employee be reduced by the individual's interim earnings. No interpretation and no "comprehensive analysis" by the arbitrator or by the PERB were necessary to discern that, by its terms and "on its face," the Back Pay Act requires an offset of interim earnings. MPD, supra note 2, 901 A.2d at 788. Arbitrator Barrett, however, *179 overlooked this provision of the very law that he relied upon in fashioning the arbitration award. Given this obvious incongruity, the PERB was not unreasonable in concluding that the award of back pay without offset was "contrary to law."
FOP further contends that the CMPA authorizes PERB to reverse an arbitral award only if the award is contrary to both "law and public policy" (italics and bold font in appellant's brief). By raising this argument for the first time in its brief to this court, FOP invites us to contravene D.C.Code § 1-617.13(b) (2001), which states that "[n]o ... objection to an order of the Board shall be considered ..., unless such ... objection was first urged before the Board."[8] Even if we were to consider FOP's argument drawing a distinction between law and public policy, it would likely be unavailing, since our decisions interpreting section 1-605.02(6) establish that an award that is contrary to a specific law ipso facto may be said to be contrary to the public policy that the law embodies. MPD, supra note 2, 901 A.2d at 789 ("a public policy alleged to be contravened ... is to be ascertained by reference to the laws and legal precedents and not from general considerations of supposed public interests") (quoting W.R. Grace & Co. v. Local Union 759, 461 U.S. 757, 766, 103 S.Ct. 2177, 76 L.Ed.2d 298 (1983)).[9]
In sum, because the PERB's decision was based on "substantial evidence" and reflects a reasonable interpretation of the CMPA, we must uphold it. Drivers, Chauffeurs, & Helpers Local Union No. 639, supra, 631 A.2d at 1215-16.
So ordered.
NOTES
[1]  See 5 U.S.C. § 5596 (2006).
[2]  Less than a month later, Arbitrator Barrett sent a letter to FOP indicating that he "inadvertently[] did not permit the offset of earnings to mitigate the back pay awarded to the grievants." He explained that he "had intended to say that the Union had not provided citation of authority to waive the normal rules of mitigation" but had made a "mistake." He offered FOP the opportunity to argue that "mitigation be waived because of the frivolous case against the grievants," but FOP declined the invitation. Instead, the parties proceeded to review by the PERB.

Although Arbitrator Barrett's letter was part of the agency record, the PERB did not cite it as a reason for its decision. Accordingly, we may not look to the letter as a basis for affirming the PERB's ruling. See Teamsters Local 1714 v. Public Employee Relations Bd., 579 A.2d 706, 709 (D.C. 1990) (we may not "affirm on a ground not relied on by the agency"). Nonetheless, we observe that by modifying Arbitrator Barrett's award, the PERB appears to have effectuated the arbitrator's true intent, rather than to have improperly "substitute[d] its judgment for the arbitrator's." District of Columbia Metro. Police Dep't. v. District of Columbia Pub. Employee Relations Bd., 901 A.2d 784, 789 (D.C.2006) (hereinafter "MPD") (citation omitted).
[3]  Our decisions acknowledge that, where an arbitrator is called upon actually to interpret the law, his interpretation merits deference, because it is the interpretation that the parties "bargained for." MPD, supra note 2, 901 A.2d at 789; see also American Postal Workers Union, AFL-CIO v. United States Postal Serv., 789 F.2d 1, 2-3 (D.C.Cir.1986) (citing United Steelworkers v. Enterprise Wheel & Car Corp., 363 U.S. 593, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960)).
[4]  FOP relies on the Board's conclusion in another case that provisions of the District Personnel Manual that mandate the offset of interim earnings from back pay awards applied only to awards made in statutory appeals (to the Office of Employee Appeals) and not to arbitration awards made prior to February 4, 2005. See District of Columbia Dep't of Corr. v. Fraternal Order of Police/Dep't of Corr. Labor Comm. (on behalf of Dexter Allen), Slip Op. No. 825 at 11-12, PERB Case No. 04-A-14 (2006). From this, FOP argues that Arbitrator Barrett's October 16, 2004 no-offset award in this case was "completely lawful."

FOP also argues that the federal Back Pay Act, including its offset requirement, simply "does not apply" to District employees. The PERB disagrees. The parties' disagreement on this point perhaps reflects the fact that the continuing applicability to District employees, of a federal personnel law that formerly was broadly applicable to District personnel matters, depends on whether the provision at issue is saved by virtue of the CMPA savings clause, D.C.Code § 1-602.04(a) (2001). The savings clause "provides a floor for benefits under the D.C. CMPA, equal to those applicable to federal employees `immediately prior' to enactment of District personnel legislation." District of Columbia v. Hunt, 520 A.2d 300, 303 (D.C.1987) (quoting American Fed'n of Gov't Employees v. Barry, 459 A.2d 1045, 1049 (D.C.1983)). In other words, "the District must retain personnel benefits and entitlements at least equal to those previously available under the federal system, even after the CMPA went into effect." Id. Given the basis for our disposition here, we need not further address the parties' dispute about this issue.
[5]  Indeed, in the Dexter Allen case, see note 4 supra, the PERB upheld an arbitral decision that awarded an employee full back pay with no deduction for interim income. The PERB explained in Dexter Allen that the arbitrator in that case had not "relied on a specific statute for awarding back pay ... that expressly requires offset."
[6]  We must sustain the PERB's reasonable interpretation "even if a petitioner advances another reasonable interpretation of the statute or if we might have been persuaded by the alternate interpretation had we been construing the statute in the first instance." Teamsters Local Union 1714, supra note 2, 579 A.2d at 711 n. 5, quoting Smith v. District of Columbia Dep't of Employment Servs., 548 A.2d 95, 97 (D.C. 1988).
[7]  FOP never argued to the Board  as it urges now  that the arbitrator's reference to the Back Pay Act was an inconsequential "mention" rather than the very foundation of the award that he fashioned.
[8]  See also D.C.Code § 1-617.13(c) (2001) (establishing that the court's jurisdiction to review a PERB order is as described in section 1-617.13(b) (2001)); see also Fraternal Order of Police MPD Labor Comm. v. Public Employee Relations Bd., 516 A.2d 501, 505 n. 5 (D.C. 1986) (court lacked jurisdiction to hear issues that had not been raised before the PERB).
[9]  Finally, FOP urges us to apply our Uniform Arbitration Act case law holding that we "will not set aside an arbitration award for errors of either law or fact made by the arbitrator." Appellant's Brief at 11, quoting Motor City Drive, L.L.C. v. Brennan Beer Gorman Monk Architects & Interiors, PLLC, 890 A.2d 233, 236 (D.C.2006) (further citations omitted), and citing Poire v. Kaplan, 491 A.2d 529, 534 (D.C. 1985). FOP's reliance on these cases is misplaced. At all times relevant to this appeal, the Superior Court has had authority to vacate an arbitral award only in limited circumstances described in D.C.Code § 16-4311 (a) (2008 Supp.) (repealed and superseded effective July 1, 2009, see D.C. Law 17-111, §§ 2(b) and 3, 55 D.C.Reg. 1847 (Feb. 29, 2008)). There also is some case authority for vacating an award where an arbitrator "manifestly disregarded the law." Schwartz v. Chow, 867 A.2d 230, 233 (D.C.2005). But, under current law, no authority permits the court to vacate an arbitrator's award because it is "contrary to law and public policy." Cf., e.g., Lincoln Nat'l Life Ins. Co. v. Payne, 374 F.3d 672, 675 (8th Cir.2004) ("Manifest disregard of the law requires something more than a mere error"). The PERB, by contrast, has express statutory authority to vacate or modify an award on that basis. See D.C.Code § 1-605.02(6) (which describes the PERB's "exclusive method for reviewing the decision of an arbitrator ..., notwithstanding provisions of [D.C.Code] §§ 16-4301 to 16-4319 [the Uniform Arbitration Act]").
