STUART, Justice.

Howard M. Schramm, Jr., appeals the March 6, 2012, judgment of the Baldwin Circuit Court approving pier-construction permits issued to Schramm's neighbors, George G. Spottswood and Amy H. Spottswood, by the Alabama Department of Conservation and Natural Resources ("DCNR") and Baldwin County even though the proposed pier would violate the 10-foot setback rule in the applicable DCNR and Baldwin County rules and regulations (appeal no. 1110794). The Spottswoods cross-appeal the order of the Baldwin Circuit Court denying their January 9, 2012, motion to alter, amend, or vacate its February 27, 2007, judgment setting the boundaries of their riparian-use area (appeal no. 1110915). We affirm.

I.

This dispute concerns the boundaries between three coterminous lots located on the eastern shore of Mobile Bay approximately one mile south of the Grand Hotel at Point Clear. In March 2005, the Spottswoods bought the middle of those lots from the Demouy family and thereafter commenced replacing the existing pier on the lot ("the Demouy pier"), which had been built in the 1950s but had been damaged by Hurricane Ivan in 2004. When it became apparent to the Spottswoods' neighbors to the south, Henry E. Reimer, Sr., Daniel E. Reimer, Sr., Regina R. Ehlert, and Melanie R. Moore (collectively referred to as "the Reimers"), that the Spottswoods intended to build their new pier to the south of where the Demouy pier had been located, the Reimers became concerned that their view of the sunset and of the Grand Hotel would be obstructed, and they accordingly commissioned a survey to ascertain the proper boundary lines for the lots, both the upland boundary line between the lots and the riparian boundary line extending out from the shore and into Mobile Bay.1 When that survey showed the upland boundary line between the lots as being in a location that significantly decreased what was believed to be the Spottswoods' water frontage and the riparian boundary line as being in a location that bisected the Demouy pier, the Reimers initiated an action seeking to establish conclusively the boundary lines set forth in that survey as the boundaries between the two lots. The Spottswoods filed a counterclaim seeking to establish the property lines in a manner consistent with their own survey, which afforded them significantly more waterfront footage. Eventually Schramm, the Spottswoods' neighbor to the north, intervened, seeking a judgment declaring the boundary lines between his lot and the Spottswoods' lot as well.

On February 27, 2007, the trial court entered a final judgment in the case. In that order, the trial court noted that the determination of the boundaries was complicated by the fact that the documentary evidence did not clearly define boundaries along the beach area, which had changed shape and grown by a minimum of approximately 50 feet and perhaps as much as 150 feet over an approximately 150-year period. Applying equitable principles, the trial court therefore held that the boundary line proposed by the Spottswoods was the proper border between their lot and the Reimers' lot, thus giving the Spottswoods ownership of a disputed triangle-shaped piece of land also claimed by the Reimers. However, the trial court also declined to apply the general rule holding that riparian boundary lines should run perpendicular to the shoreline because doing so would have placed the riparian boundary between the Spottswoods and the Reimers directly through the Reimers' pier, which had existed since the 1950s and which, when built, was undisputedly south of a line running perpendicular to the shore where the Spottswood and Reimer parcels met. Thus, the trial court held that the riparian boundary line should instead extend out into the water at the same angle as the upland boundary line.

The trial court also held that both the upland and riparian boundary lines between Schramm's lot and the Spottswoods' lot had been defined in a 1956 agreement between their predecessors in title. That agreement also required any pier or similar structure constructed on Schramm's lot to observe a 25-foot setback along the riparian boundary line with the Spottswoods, which line, pursuant to the general rule, extended perpendicular from the shore. The trial court further held that the 1956 agreement imposed no similar setback requirements upon the owners of the Spottswoods' lot.

Once the riparian boundary lines of the Spottswood property were established, the result was that the Spottswoods had riparian rights to a triangle-shaped area in front of their property bordered by the shore on the east and the above-described riparian boundary lines on the north and south until they intersected at a point approximately 105 yards offshore. With regard to the placement and style of any pier constructed by the Spottswoods, the trial court held that the Spottswoods could proceed with the construction of a new pier without any limitation upon the height, structure, or materials used, provided (1) that they complied with all applicable state and federal permitting requirements and (2) that they built the pier in the same general footprint of the Demouy pier — even though the Demouy pier had in fact encroached to a small extent into waters as to which Schramm had riparian rights. Finally, the trial court noted that it retained jurisdiction "to determine any subsequent issues regarding the establishment or description of the land and riparian boundary lines decreed herein or the Spottswoods' construction of their pier."

The Spottswoods subsequently appealed the judgment of the trial court, arguing that the court erred in its determination of their riparian boundary line with the Reimers and in requiring them to build any new pier within the footprint of the Demouy pier; the Reimers cross-appealed, arguing that the trial court erred in its determination of the upland boundary line between their lot and the Spottswood lot. On July 24, 2009, in Spottswood v. Reimer, 41 So.3d 787, 796-98 (Ala.Civ.App.2009), the Court of Civil Appeals affirmed the trial court's judgment insofar as it established both the upland and riparian boundaries between the Spottswood and Reimer lots; however, it reversed the trial court's judgment to the extent it required the Spottswoods to build any future pier in the footprint of the Demouy pier, holding that that restriction was in violation of § 33-7-50, Ala.Code 1975, which, this Court held in Ex parte Cove Properties, Inc., 796 So.2d 331, 334 (Ala.2000), authorizes owners of riparian lands to construct a pier in navigable waters in front of their property subject only to harbor and pier lines established by the United States or the State of Alabama and the additional caveat that the pier not unreasonably obstruct navigation.

On approximately February 10, 2010, the Reimers began seeking permits to begin repairing their pier, which had been damaged in August 2005 during Hurricane Katrina, by preparing (1) a joint application to the United States Army Corps of Engineers and the Alabama Department of Environmental Management; (2) an application to DCNR; and (3) an application to Baldwin County. On February 26, 2010, the Reimers submitted a copy of their applications and plans to the trial court, the Spottswoods, and Schramm, asking the trial court to confirm that the construction of their pier was in compliance with the trial court's February 27, 2007, order. On April 19, 2010, the trial court entered an order confirming that the Reimers' proposed pier did not violate its earlier judgment and again stating that it would retain jurisdiction "to review any application hereafter submitted by [the Spottswoods] for the construction of their pier."

Subsequently, however, the Spottswoods filed an objection to the Reimers' proposal with DCNR, arguing that the Reimers' proposed pier would come within 10 feet of the riparian boundary separating their riparian-use area, in violation of DCNR rules requiring all piers on State-owned submerged land to be "setback 10 feet from the riparian lines of adjacent property owners," Ala. Admin. Code (Department of Conservation and Natural Resources), Rule 220-4-.09(4)(b)(11), as well as a similar Baldwin County regulation. The Reimers thereafter requested the trial court to intervene, arguing that they were rebuilding their pier in the footprint on which it had existed for over 50 years, with the exception of a 3-foot addition to the boat lift — the boat lift being the only part of the pier within 10 feet of the riparian boundary — that had been made in 1998 with the approval of the Demouy family, the Spottswoods' predecessors in title. However, the Reimers subsequently conceded the issue and redrew their plans to place the boat lift on the south side of their pier so as to completely prevent any portion of their pier from intruding into the 10-foot setback area.

The Spottswoods thereafter filed for permits to build their own pier, receiving the permits in January and February 2011. Those permits approved the Spottswoods' plans to build a pier just inside the riparian boundary line separating the Spottswoods' and Schramm's riparian-use areas. In other words, the proposed pier left essentially no setback area on the Spottswoods' side of the riparian boundary line. In an affidavit explaining the decision to approve the Spottswoods' plans in spite of the lack of the required 10-foot setback, DCNR employee Jeff Jordan stated:

Schramm became aware of the Spottswoods' plans in April 2011 after he was given a copy of the plans by a member of the Reimer family. A short time later, the Spottswoods commenced construction of their pier, and, on May 9, 2011, Schramm asked the trial court to set a hearing to review the plans for the Spottswoods' pier. The Spottswoods thereafter voluntarily stopped construction on their pier, and the Reimers and Schramm subsequently filed a formal joint motion asking the trial court to prohibit the Spottswoods from building the planned pier based on the failure to observe the 10-foot setback required by DCNR and by Baldwin County regulations.2

On January 9, 2012, the Spottswoods filed a motion asking the trial court to amend its February 27, 2007, order setting the riparian boundaries for the water in front of their lot because, they argued, pursuant to § 9-12-22, Ala.Code 1975, they were entitled to grow and harvest oysters "in the waters in front of their land to the distance of 600 yards from the shore." However, the Spottswoods argued, the riparian boundaries set by the trial court caused their riparian-use area to terminate only 105 yards from the shore, thus prohibiting them from the full enjoyment of their rights under § 9-12-22. The trial court conducted an ore tenus evidentiary hearing on all pending matters on March 2, 2012, and on March 6, 2012, issued separate orders denying both the Reimers' and Schramm's joint request to invalidate the pier permits issued the Spottswoods and the Spottswoods' motion to amend its February 27, 2007, judgment setting their riparian boundaries. On March 19, 2012, Schramm appealed the judgment entered against him, and, on April 11, 2012, the Spottswoods appealed the judgment entered against them.

II.

This Court explained the standard of review applicable to Schramm's appeal in Ex parte City of Fairhope, 739 So.2d 35 (Ala.1999), in which we considered the City of Fairhope's argument that the Court of Civil Appeals had improperly reversed the judgment of the circuit court affirming the City of Fairhope's issuance of a permit authorizing a second-floor addition to a grandfathered nonconforming garage that did not meet the side-yard setback requirement. We stated then:

739 So.2d at 38. The standard of review applicable to the Spottswoods' cross-appeal is the standard of review applicable to the denial of a Rule 59(e), Ala. R. Civ. P., postjudgment motion to alter, amend, or vacate a judgment. "Whether to grant relief under Rule 59(e), Ala. R. Civ. P., is within the trial court's discretion." Bradley v. Town of Argo, 2 So.3d 819, 823 (Ala.2008).

III.

On appeal, Schramm argues that DCNR's issuance of a permit to the Spottswoods for construction of a pier violated the agency's own rules and that DCNR's decision was arbitrary and capricious.3 Specifically, he cites Ala. Admin. Code (Department of Conservation and Natural Resources), Rule 220-4-.09(4)(c)(4), which provides:

It is undisputed that none of the listed exceptions apply here, and Schramm argues that it was accordingly error for DCNR to base its decision on an unenumerated exception. The Spottswoods, however, cite DCNR employee Jordan's testimony that Ala. Admin. Code (Department of Conservation and Natural Resources), Rule 220-4-.09(4)(c)(1), authorizes DCNR to decline to enforce a rule if doing so would "unreasonably infringe upon the traditional, common-law riparian rights of upland property owners adjacent to state-owned submerged lands." We agree that Rule 220-4-.09(4)(c)(1) provides another basis on which DCNR can grant exceptions to the 10-foot setback requirement; however, this conclusion in turn raises the issue whether enforcing the 10-foot setback requirement against the Spottswoods would infringe upon a common-law riparian right held by them. Schramm argues that it would not; the Spottswoods argue that it would.

Jordan testified that DCNR granted the Spottswoods' application for a pier permit because enforcing the setback requirement would infringe upon the general common-law right held by all owners of riparian property to be able to "wharf out" to waters of a reasonable navigational depth. Schramm disputes that such a common-law riparian right exists; however, caselaw reveals that this common-law right has in fact been recognized in most jurisdictions, including Alabama. In Cove Properties, Inc. v. Walter Trent Marina, Inc., 796 So.2d 322, 326-27 (Ala.Civ.App.1999), reversed in part on other grounds, 796 So.2d 331 (Ala.2000), the Court of Civil Appeals stated:

Thus, the Spottswoods do have the common-law right to build a pier in the waters in front of their property extending out to the point of navigability, and, under Rule 220-4-.09(4)(c)(1), DCNR may interpret and implement its rules in a manner that will respect that right.

However, even if this Court does recognize the Spottswoods' right to wharf out to the point of navigability, Schramm nevertheless argues that DCNR's approval of their permit application was arbitrary and capricious because, he argues, there is no evidence indicating that disregarding the 10-foot setback along their riparian boundary enables them to wharf out to a deeper part of the bay. Although it is true that there is no specific evidence of water depths or offshore slopes indicating that the Spottswoods will reach deeper water by placing their pier along the riparian boundary, we nonetheless conclude that DCNR's decision to issue the permit is reasonable in light of that goal.

In his affidavit, Jordan stated that, after reviewing the boundary lines set by the trial court and considering "the unique near shore dynamics of the Mobile Bay along that area," he concluded that it may not be possible for the Spottswoods to reach reasonable navigable depths and still observe the required setbacks. He further stated that it was DCNR policy to allow riparian property owners to construct piers similar to those maintained by neighboring properties with similar shoreline widths, and the evidence and maps in the record indicate that the Spottswoods' proposed pier extends approximately as far into Mobile Bay as the piers of both Schramm and the Reimers. Presumably, those piers extend to the point of navigability, because they have no right to extend any further. Cove Properties, Inc. v. Walter Trent Marina, Inc., 796 So.2d at 326-27; see also Great American Ins. Co. v. Tugs "Cissi Reinauer", 933 F.Supp. 1205, 1218 (S.D.N.Y.1996) ("The right to construct a wharf derives from the right of access to `navigable' or `deep' water. 1 H.P. Farnham, Water and Water Rights § 62. For that reason, `as soon as the point of navigability is reached, the purpose of the pier is fulfilled, and the right to construct it ceases at that point.' Illinois Cent. R.R. Co. v. Illinois, 146 U.S. 387, 13 S.Ct. 110, 36 L.Ed. 1018 (1892)."). The maps in evidence indicate that moving the Spottswoods' proposed pier south of the riparian boundary line any significant distance would immediately move it within the setback area for the riparian boundary line adjoining the Reimers' riparian-use area. Thus, the only way the Spottswoods may have a pier similar in length to the pier of either Schramm or the Reimers is to disregard the setback requirements on either one side or the other. DCNR had a reasonable basis upon which to waive the setback on the Spottswoods' northern riparian border adjacent to Schramm's riparian-use area instead of the southern riparian border because of the 25-foot setback Schramm maintains on his side of the riparian boundary line, thus assuring that all three piers are separated by a reasonable distance, given the unique circumstances of these lots. Moreover, we note that the Demouy pier had also apparently encroached upon the 10-foot setback — and to a minor extent over the riparian boundary-line — for several decades, and, for all that appears, this was never the subject of dispute among the parties. For these reasons, we cannot conclude that DCNR's decision to approve the Spottswoods' plans for construction of the pier was clearly unreasonable, arbitrary, or without a rational basis, and we accordingly affirm the judgment of the trial court denying Schramm and the Reimers' request that the Spottswoods be prohibited from building a pier consistent with that permit.

We also affirm the order of the trial court denying the Spottswoods' motion to alter, amend, or vacate its February 27, 2007, order setting the boundaries of the Spottswoods' riparian-use area. The Spottswoods argue that their motion, filed almost five years after the trial court's final judgment, was nevertheless timely and appropriate because the trial court stated in that order that it would retain jurisdiction over the case to determine any "subsequent issues" that arose regarding the boundary lines. We disagree. The Spottswoods' motion does not raise any new issue because determining the riparian boundary lines of the Spottswoods' property was one of the central issues in this case from its inception. Rather, the Spottswoods' motion is an attempt to advance a new argument in order to revisit an issue already decided by the trial court in its February 27, 2007, order, which decision was affirmed by the Court of Civil Appeals in Spottswood, 41 So.3d at 797 ("[W]e affirm the trial court's judgment insofar as it determines that the riparian boundary line is an extension of the Spottswood line."). This they cannot do. See Ex parte S.T.S., 806 So.2d 336, 341 (Ala.2001) ("The issues decided by an appellate court become the law of the case on remand to the trial court, and the trial court is not free to reconsider those issues. Murphree v. Murphree, 600 So.2d 301 (Ala.Civ.App.1992)."). The trial court did not exceed its discretion in rebuffing the Spottswoods' attempt to relitigate this issue.

IV.

In appeal no. 1110794, Schramm appealed the judgment of the trial court approving the pier-construction permit issued to the Spottswoods by DCNR, arguing that DCNR's decision to issue its permit was arbitrary and capricious. However, because the evidence indicates that DCNR had a rationale basis for its decision, we affirm the judgment of the trial court. In appeal no. 1110915, the Spottswoods cross-appealed from the order of the trial court denying their motion to alter, amend, or vacate its February 27, 2007, judgment setting the boundaries of their riparian-use area. Because that motion sought to relitigate an issue already decided by the trial court and the Court of Civil Appeals, we affirm that order as well.

1110794 — AFFIRMED.

1110915 — AFFIRMED.

MALONE, C.J., and PARKER, SHAW, and WISE, JJ., concur.