The plaintiffs, Richard and Christine Spillane (Spillanes), objected to the presence of two small boats moored on tidal flats within sight of their house located on Black Beach in the town of Manchester-by-the-Sea (town). Confident of their right to do so and exercising self-help, they had the moorings removed. Thereafter they sought a declaration under G. L. c. 231A in the Land Court to establish their ownership of the tidal flats, as well as a declaration that they are entitled to the exclusive use and control of the flats to the low water mark.3 As defendants, they named Samuel Adams, James O. Welch, Jr., and the town.4 The Spillanes subsequently amended their complaint to add the Commonwealth as a defendant.5 The offending vessels, a fourteen-foot sailboat and a seventeen-foot motor boat, were owned by Adams and Welch, respectively.
In response to the complaint, Adams filed a counterclaim seeking costs to replace his mooring. Welch filed a counterclaim alleging that the plaintiffs had no ownership rights in the flats or, alternatively, asserting the existence of a prescriptive easement permitting him to moor his boat. Finally, the Commonwealth *380counterclaimed, seeking a declaration of the boundaries of the flats under G. L. c. 240, § 19.
At trial, the Spillanes’ claim of ownership was based on a deed dated November 3, 2003, from Wendell Weyland, trustee of the ACK Trust. Their evidence traced their chain of title in the upland and flats to a deed into Elizabeth H. Dewart dated May 13, 1902.6
In opposition the town proffered evidence of a 1640 grant of land, originally part of Salem and now comprising the town, which established the town and vested it with title to the transferred land (1640 grant). The town asserted that the 1640 grant included the upland tract, now designated as parcel 3. Because the 1640 grant was followed closely in time by the Colonial Ordinance of 1641-1647 (Colonial Ordinance) extending ownership of all upland parcels into the corresponding tidal flats, the town asserted that the Spillanes’ predecessors in title were not the rightful owners of the flats. As described infra, the town further supported its claim with additional evidence, including a 1919 title examiner’s report (1919 report) prepared for a Land Court registration case originally intended to quiet title to the parcel here at issue, among others. The judge determined that (1) the town, rather than the Spillanes, owned the flats, (2) the boundary of the flats was the mean low water mark in accordance with the National Geodetic Vertical Datum (NGVD) standards, and (3) the Spillanes were liable to Adams for $145 in damages for the removal of his mooring.7
Subsequently, the town filed two postjudgment motions. The first, pursuant to Mass.R.Civ.P. 15(b), 365 Mass. 761 (1974), sought to amend the town’s responsive pleading to assert a counterclaim against the Spillanes to quiet title to the upland in the town. The second, pursuant to Mass.R.Civ.P. 52(b), as amended, 423 Mass. 1402 (1996), and Mass.R.Civ.P. 59, 365 Mass. 827 (1974), requested an amendment to the findings and *381judgment to reflect the town’s ownership of the upland. The judge denied both motions.
The Spillanes timely appealed the Land Court judge’s decision8; the town timely cross-appealed, challenging the denial of its postjudgment motions. We affirm.
Discussion. 1. Ownership of the flats, a. The Spillanes’ claim. We turn first to the Spillanes’ contention that the judge erred in rejecting their claim to ownership of the flats. They assert principally that the judge’s ruling is based on an incorrect interpretation of Tappan v. Burnham, 8 Allen 65 (1864), and, alternatively, that the judge improperly took judicial notice of the conclusions set forth in the 1919 report.
We accept a judge’s findings of fact unless they are “clearly erroneous.” Mass.R.Civ.P. 52(a), as amended, 423 Mass. 1402 (1996). Because a trial judge is in the best position to judge the weight and credibility of the evidence, a finding of fact “will not be deemed ‘clearly erroneous’ unless the reviewing court on the entire evidence is left with the firm conviction that a mistake has been committed.” New England Canteen Serv., Inc. v. Ashley, 372 Mass. 671, 675 (1977). In evaluating the judge’s decision, we are mindful that the plaintiffs bore the burden of affirmatively establishing title, and that simply “demonstrating the weaknesses or nonexistence of the defendants’ title” is insufficient. Sheriff’s Meadow Foundation, Inc. v. Bay-Courte Edgartown, Inc., 401 Mass. 267, 269 (1987).
As stated, the Spillanes traced their title to 1902. They contend that this lineage is more than adequate to establish ownership, citing G. L. c. 93, § 70, and the title requirements of the Real Estate Bar Association.9 In the absence of countervailing *382evidence they would be correct, but here they were confronted with a claim predating theirs by several centuries. See Sheriff’s Meadow Foundation, Inc. v. Bay-Courte Edgartown, Inc., supra at 269-270 (the length of a chain of title holds no weight where a prior, superior title exists).
The town’s evidence was that in 1640 Salem vested title through the grant in all land that comprises the present-day town.10 See Tappan v. Burnham, supra at 71. The Spillanes contest the judge’s application of Tappan to this case because Tappan does not preclude explicitly the possibility that parcel 3 in the instant case had been conveyed to another party before the 1640 grant by Salem. There is simply no evidence in the record to support this speculation, and the judge was entitled to draw the inference that parcel 3 was part of the 1640 grant.
Subsequent to the 1640 grant, as stated, the Massachusetts Bay Colony passed the Colonial Ordinance extending the town’s interest in shore-front property to the tidal flats.11 Id. at 71-72. As described below, the town also demonstrated the continuation of title established by the 1640 grant and Colonial Ordinance into the twentieth century. Thus, in the absence of evidence that the flats were transferred out of the land subject to the 1640 grant before the grant was made, or that the town alienated or lost title to either the upland or the flats prior to 1902, we recognize a presumption that title continues in the town. Id. at 72. See Porter v. Sullivan, 7 Gray 441, 445 (1856) (“[I]n the absence of any proof of the alienation of the one without the other, the presumption of law is, that the title to the flats follows that of the upland on which they he, and proof of title to the upland establishes a title to the flats”). In sum, to defeat the presumption and satisfy their burden, the Spillanes were required to provide evidence of a transfer by Salem of the upland prior to 1640 or a transfer of the *383flats prior to 1641 (so that the 1640 grant or the Colonial Ordinance can be ruled out of the chain of title) or, alternatively, a transfer of either out of the town’s ownership after the year 1640 and before 1902.
The town presented additional evidence from previous Land Court filings; we consider the two principal cases.
(i) Registration case no. 7143. The town initiated case no. 7143 in 1919 to establish title to various parcels of property, including upland parcels on Black Beach, of which parcel 3 was one. The sole objection to the town’s claims was lodged by Elizabeth Dewart, a predecessor in interest to the Spillanes. Accordingly, the town’s claim to parcel 3 was severed from case no. 7143,12 which then proceeded to judgment based on the 1919 report supporting the town’s claims. The 1919 report concluded that the town owned the upland parcels under review. At the time it was submitted, the 1919 report included parcel 3, but as noted that parcel was subsequently severed from the original registration case.
In the proceeding below, the town pointed to the rational inference, adverse to the Spillanes, permissibly derived from the 1919 report in case no. 7143 which applied factually, albeit not legally binding, to parcel 3. The Spillanes, by contrast, emphasized that registration case no. 7143 did not decide the question of title to parcel 3, and the judge below acknowledged as much, stating that case no. 7143 “no more determined title [to parcel 3] than if that parcel were not part of the original case.” The judge nevertheless considered the conclusions contained in the 1919 report as pertinent to ownership of parcel 3, and we conclude that she was correct in so doing. Although the 1919 report lacks direct legal applicability to parcel 3, resulting as it does from a procedural history that simply left the town’s claim to that tract unresolved, that fact does not preclude consideration here of the research the report contains.
The Spillanes also object to the judge’s use of the 1919 report on the separate ground that it was not properly admitted in evidence in the instant case for the truth of its contents, but *384only to demonstrate the fact that it had been performed.13 To the extent this is an assertion that the Spillanes are not collaterally estopped by the conclusions contained in the 1919 report, it is correct, but unavailing. A copy of the case file was admitted in evidence by agreement of all parties; no conditions were attached. The judge was entitled to examine the evidence — including the 1919 report — and make findings based on that evidence. The record, including the fact that parcel 3 was not severed from the registration case until three months after the 1919 report was submitted, generously supports her finding. The record contains no objection by counsel for the Spillanes, or for that matter by any party, setting forth an articulated basis to limit the relevance of the evidence.14 We note as well that counsel for the Spillanes cross-examined the town’s expert on the applicability of the 1919 report to parcel 3, thereby placing the issue in factual, not just legal, contention and opening the door to testimony that the title report supports the town’s position.15
(ii) Registration case no. 24523. Russell Dewart, the son of Elizabeth Dewart, initiated registration case no. 24523 in 1953 to establish title to parcel 1, claiming appurtenant rights in Black Beach and the accompanying flats (parcels 3 and 4). After receiving the title examiner’s abstract, the Land Court judge assigned to the case wrote to Dewart’s counsel suggesting that documents in the record indicated that ownership “between low water mark and high water mark and perhaps up to the beach is in the Town.” In fact, numerous plans introduced below *385contained notations reflecting the probable ownership of the beach and flats in the town. For example, the judge could properly draw an inference from Plan 24523B, which lists Black Beach as belonging to the “inhabitants of Town of Manchester.” Likewise, registration plans for case no. 1398,16 referenced in the letter to Dewart’s counsel, when read together, suggest ownership in the town. The final decree issued in case no. 24523, though limited to registration of parcel 1, described the parcel as bounded southwesterly “by land now or formerly in the Inhabitants of Town of Manchester (Black Beach).”
Again, the town emphasized the inferences adverse to the Spillanes to be drawn from the title examiner’s report in case no. 24523 and from the judge’s accompanying letter to counsel. The Spillanes highlight the qualified nature of the title examiner’s report and, as with case no. 7143, point to the case’s lack of conclusive legal application to the case at bar. The trial judge acknowledged the equal import of all submitted Land Court case filings on the issue of title.17 As with case no. 7143, the entirety of case no. 24523 was admitted in evidence by agreement, and the judge properly could rely on its contents. While the inferences to be drawn from the documents contained in case no. 24523 are more tenuous than those in case no. 7143 (in which title to parcel 3 was directly before the court, at least at the outset of the proceedings) their probative admissibility is no less apparent.
In sum, there was ample evidence to support the judge’s finding that the Spillanes had failed to establish their ownership of the tidal flats.18
b. The town’s title to the tidal flats. Based on the evidence recited above, the judge ruled that the Spillanes had failed to establish title to the flats; she also concluded that title is in the town.19 There was no error in these determinations.
*386“One of the principal purposes of the declaratory judgment law, G. L. c. 231 A, is to settle completely the controversy submitted for decision.” Kilroy v. O’Connor, 324 Mass. 238, 242 (1949). Where such judgment or decree, if rendered or entered, would not terminate the uncertainty or controversy giving rise to the proceedings, or for other sufficient reasons, the court may refuse to render or enter a declaratory judgment or decree. G. L. c. 231 A, § 3. But “when an action for declaratory relief is properly brought, even if relief is denied on the merits, there must be a declaration of the rights of the parties.” Boston v. Massachusetts Bay Transp. Authy., 373 Mass. 819, 829 (1977). See Dupont v. Dracut, 41 Mass. App. Ct. 293, 297 (1996). In sum, the Spillanes put ownership of the flats in issue, and the judge had ample latitude to establish the town’s title.
2. Low water mark. The Spillanes also claim error in the judge’s determination that the low water mark should be measured by reference to mean low water as established by the NGVD. Having established which party had rightful title to the flats, it was appropriate under G. L. c. 231A for the judge to adjudicate the boundaries to which the title applied, especially where it was disputed by the parties. See Boston v. Massachusetts Bay Transp. Authy., supra; Dupont v. Dracut, supra.
No definitive standard for tidal marks has been adopted in our appellate case law, and we take this opportunity to do so. Indeed, for several centuries the use of the term “low water mark” to establish property rights has been emblematic of the difficulty we encounter in seeking to apply legal precision to natural forces.20 This problem has had greater consequence in Massachusetts than elsewhere because our law gives waterfront property owners extended rights to the coastline and to tidal areas, more so than the laws of most States. In order to encourage what was deemed the productive use of waterfront property, i.e., the construction of wharves and piers,21 the Colonial Ordinance assigned rights in *387tidal flats to the owners of the adjoining uplands.22 Those rights extended to the “low water mark” or to 100 rods below high water, whichever was the shorter distance.
As the parties recognize, tidal range is inconstant and unpredictable. See, e.g., Eldridge, Tide and Pilot Book 10 (136th ed. 2010) (“[Vjigilance and prudence should govern the decisions of the navigator, and . . . experience shows that tide and current predictions are approximate to begin with”). See also Commonwealth v. Roxbury, 9 Gray 451, 482-483 (1857) (extensive discussion of English common-law principles holding that “the title to flats was in the king,” and defining flats as bounded landward by “the medium line between the ordinary line of high water in ordinary spring tides at the full and change of the moon, and the ordinary line of high water at neap tides, at about midway in time between the full and change of the moon”).
The difficulty (effectively conceded in the language of Commonwealth v. Roxbury, quoted above) of establishing boundary lines for irregular and continually shifting shorelines resulted historically in the forensic use of three separate semantic formulations to locate the “low water mark”: (1) “extreme low water line,” (2) “the low water mark that results from usual causes and conditions,” and (3) “the mean low water mark.” See generally Rochwood v. Snow Inn Corp., 409 Mass. 361 (1991), and cases cited therein. These terms were, in turn, subjected to further semantic refinement in repeated efforts, reminiscent of King Canute, to stop the tide in one place.23 As one judge of the Land Court succinctly stated in reference to tides, “[a]ll of this may *388sound precise, but it is not. ‘The tide is an alternating rise and fall in sea level produced by the gravitational force of the moon and sun. Other non-astronomical factors, such as meteorological forces, ocean floor topography, and coast line configuration, also play an important role in shaping the tide.’ ”24 Houghton v. Johnson, 14 Mass. Land Court Rptr. 442, 446 (Land Court No. 308323 [KCL], Aug. 9, 2006), S.C., 71 Mass. App. Ct. 825 (2008), quoting from Brown, Boundary Control and Legal Principles 184 (4th ed. 1995).
The most recent case to address the issue is Rockwood v. Snow Inn Corp., supra. Referring to the case law cited above, see note 23, supra, the court in Rockwood acknowledged that there is no “recognized line to which the tide usually ebbs. . . . The line of low water, like the line of high water, is gradually and constantly changing from day to day in different parts of the month, and in different parts of the year, from the highest spring tides to the lowest neap tides.” Id. at 369. The court in Rockwood, however, took the first step toward simplification by eliminating one approach, concluding that the waterfront property in question did “not extend to the ‘extreme low water line’ as that term is used in modem tidal charts to reflect the lowest level ever reached by the sea at that location, and we overrule any of our prior cases to the extent, if any, that they may imply that our law is otherwise.” Id. at 370. We are left therefore with two remaining options for locating the mark: “the low water mark that results from usual causes and conditions,” and “the mean low water mark.”
In this case the option we select not only marks the boundary of the disputed flats, it also determines whether Adams’s mooring was within the area of the flats or seaward of them. The Spillanes presented testimony from an expert witness who had determined the low water mark by planting poles at the water’s edge as the tide retreated until it reached its lowest point during a period the witness characterized as subject to “usual causes and conditions.” In defense of this methodology (which unsurprisingly placed the mooring within the flats) the Spillanes point to the fictional nature of “mean low water” in the sense *389that low tide may never actually be found at that level.25 They point out that their expert’s use of poles, by contrast, provides a location for low water that has been demonstrated to exist on at least one occasion.
The town, in opposition, proposes the use of “mean low water” as determined by the NGVD. “Mean low tide” is defined as “[t]he average of all low tides — both low and lower low — over a fixed period.” Black’s Law Dictionary 1619 (9th ed. 2009). The two approaches remaining after Rockwood thus provide a distinct contrast between a real, but continually changing, position on the one hand, and a fictional location that will be relatively constant on the other.
Faced with this choice, we conclude that the Spillanes’ reliance on a particular measurement taken at one point in time is contrary to a basic purpose of property law. Boundaries should be capable of determination with relative ease, rather than greatly subject, as here, to weather and the phases of the moon.
This is not the first occasion on which a judge of the Land Court has determined that “mean low water,” as established by the NGVD, is the appropriate standard:
“For purposes of setting boundaries, the greatest need is certainty. The best way to establish a clear line which will be: (a) respected by the parties (because it is based on objective data), and (b) easiest to enforce (because its results are repeatable), is to use the Mean High Water Elevation and Mean Low Water Elevation lines, placed according to NGVD data .... While I am not aware of any appellate court decision that has yet adopted this standard, I believe it is the standard that those courts will adopt when it is presented to them.”
Houghton v. Johnson, 14 Mass. Land Court Rptr. at 447 (Land Court No. 308323 [KCL]) (footnote omitted).26
*390In sum, the certainty provided by the NGVD is as desirable for the landowner as for the navigator. Mean water level is a commonly employed reference and is the basis for datum printed on nautical charts issued by the National Oceanic and Atmospheric Administration.27 By contrast, use of the much more subjective “usual causes and conditions” advocated by the Spillanes provides little predictive value, and creates the need for case-by-case adjudication. The judge properly exercised her discretion in her use of the NGVD mean low water datum as the “low water mark,” hence the seaward boundary of the flats.28
3. Motions to amend answer and judgment. As we noted earlier, the town has cross-appealed, alleging that the trial judge abused her discretion in denying several posttrial motions, the purpose of which was to assert an affirmative claim of ownership to the upland. We review the judge’s decision for an abuse of discretion, though consistent with the axiom that “a motion to amend should be allowed unless some good reason appears for denying it.” Afarian v. Massachusetts Elec. Co., 449 Mass. 257, 269 (2007), quoting from Castellucci v. United States Fid. & Guar. Co., 372 Mass. 288, 289 (1977). “[Prejudice to the non-moving party is the touchstone for the denial” of such motions. Homed v. Fadili, 408 Mass. 100, 105 (1990), quoting from Goulet v. Whitin Mach. Works, Inc., 399 Mass. 547, 550 n.3 (1987).
The judge did not err in denying the motions. Title to the upland was not placed in issue by any party prior to judgment; *391to the extent that title to the flats implies title to the upland, the town explicitly rejected any such claim in open court. See, e.g., Jones v. Wayland, 374 Mass. 249, 253 n.3 (1978), quoting from Kagan v. Levenson, 334 Mass. 100, 106 (1956) (“The theory of law on which by assent a case is tried cannot be disregarded when the case comes before an appellate court for review of the acts of the trial judge”).
All of the evidence ties ownership of the flats to ownership of the uplands.29 Accordingly, it remains unclear on this record why the town now appeals the denial of its posttrial motions which unnecessarily sought a result that had already been impliedly achieved, albeit in the face of initial protestations of disinterest.30
In denying the motions, the trial judge emphasized the town’s repeated assertions throughout the pretrial stages that it was not affirmatively seeking to quiet title, but rather was challenging the Spillanes’ claim to title. The Spillanes allege that the town’s contentions on this point altered their trial strategy. While we reserve judgment on the potential success of any additional claims or evidence the Spillanes might have presented, we conclude that the trial judge did not err in denying the town’s motions based on its repeated assurances that it was not seeking to quiet title. The town had ample opportunity to raise an affirmative claim of ownership to the upland and declined to do so on multiple occasions.31 We have no basis to know whether evidentiary submissions would support a finding that severs title to the upland from title to the flats, and we offer no opinion on the town’s ability to bring an action to quiet title in the future.
4. Damages. Given our conclusion that title to the tidal flats *392was properly found to reside in the town, we find no error in the ruling below that the Spillanes are liable to defendant Adams for damages in the amount of $145.
Judgment affirmed.
Order denying motion to amend judgment and findings affirmed.
*393Appendix.
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The Spillanes contend they are the owners of four contiguous parcels in the town: parcel 1, on which their home is located; parcel 2, which includes both upland and tidal flats on Black Beach; parcel 3 (upland), a portion of Black Beach directly south of parcel 1 and extending to the mean high water mark; and parcel 4 (the flats), consisting of tidal flats south of parcel 3. A sketch of the area is attached to this opinion as an Appendix.
The complaint originally included as defendants Adele Q. Ervin and Catherine C. Lastavica. Lastavica did not participate in the case below, and a motion to dismiss the case against Ervin was allowed by the Land Court on June 8, 2007. Neither is a party to this appeal.
The Commonwealth sought to protect the rights of the public pursuant to the public trust doctrine, “an age-old concept with ancient roots . . . expressed as the government’s obligation to protect the public’s interest in . . . the Commonwealth’s waterways.” Trio Algarvio, Inc. v. Commissioner of the Dept. of Envtl. Protection, 440 Mass. 94, 97 (2003). Under the public trust doctrine, the Commonwealth holds tidelands in trust for traditional public uses of fishing, fowling, and navigation. Fafard v. Conservation Commn. of Barnstable, 432 Mass. 194, 198 (2000).
While there was additional evidence tracing the Spillanes’ chain of title to the mid-nineteenth century, they did not rely on any proof of ownership prior to 1902 for purposes of this case. In any event, that evidence does not affect our analysis.
The trial judge explicitly indicated that her decision concerned the ownership and location solely of the flats, noting that “the upland is not at issue.”
Specifically, the Spillanes allege on appeal that the judge erred in (1) ruling that the town owned the flats, (2) employing the NGVD mean low water mark as the seaward boundary of the flats, and (3) finding that they were liable to defendant Adams for $145.
General Laws c. 93, § 70, as amended by St. 1994, c. 350, § 3, establishes a requirement of a title examination “which covers a period of at least fifty years with the earliest instrument being a warranty or quitclaim deed,” for purposes of title certification to mortgaged premises. Title Standard No. 1 of the Real Estate Bar Association for Massachusetts states that “[i]t is sufficient if the title examination covers a period of fifty years and the starting point is a warranty, quitclaim, or duly authorized or empowered fiduciary’s deed which on its face does not suggest any defects.” Eno & Hovey, Real Estate Law c. 58, at 249 (4th ed. 2004).
The 1640 grant covered land in a settlement then named Jeffry es Creeke, now known as Manchester-by-the-Sea.
Specifically, the Colonial Ordinance provided shore front owners with title to the “low water mark” or 100 rods below high water, whichever was higher: “It is Declared, That in all Creeks, Coves and other places, about and upon Saltwater, where the Sea ebbs and flowes, the proprietor of the land adjoining, shall have propriety to the low-water mark, where the Sea doth not ebb above a hundred Rods, and not more wheresoever it ebbs further.” Opinion of the Justices, 365 Mass. 681, 685 (1974), quoting from The Book of General Lawes and Libertyes 50 (1649).
A separate case (no. 8537), established to resolve ownership of parcel 3, was not pursued by the town and eventually was dismissed without prejudice.
The judge stated that she accepted “the conclusion embodied in the title abstract in Registration Case 7143, which was reintroduced as evidence in this case.”
Counsel for the Spillanes conceded that the judge was entitled to take judicial notice of case no. 7143 “so long as there’s a relevance to it.” By contrast, counsel objected to testimony introduced by opposing counsel on more than 160 occasions during a time span totaling slightly in excess of one trial day, and in the face of conscientious efforts by the judge to preserve a coherent flow to the proceedings. In this context we do not view the failure to register an objection to any particular use of case no. 7143 as insignificant.
The town’s expert stated, “I believe the petition described the entirety of Black Beach when the petition was first initially filed which included parcel three,” and in answer to continued questioning, “[w]hat [the report] does do, by filing the petition and describing all the lots, including parcel three, the inference is that it is included.”
Registration case no. 1398 sought to register land abutting parcel 1, a tract to the east of the upland.
The judge stated that “[ajnything in the Land Court records of any of these registration cases that involve any piece of [the] property [at issue], in my view, is relevant to the issue of title that is in front of me in this case.”
We note that the record contains various additional deeds and registration plans from which the judge could also draw an inference of the town’s ownership; these are largely duplicative of the evidence described supra, and we do not discuss them separately.
The town initially asserted that its position was limited to opposing the *386Spillanes and did not include establishing its own right to title. It then reversed course by filing postjudgment motions seeking to quiet title to the upland in the town and now appeals from the denial of those motions. See part 3, infra.
This observation of course applies equally to “high water mark” which is, however, not at issue here.
“[T]he king held the sea shores as well as the land under the sea . . . for the use and benefit of all the subjects, for all useful purposes, the principal of *387which were navigation and the fisheries.” Commonwealth v. Roxbury, 9 Gray 451, 483 (1857).
The Colonial Ordinance, now in existence for some 370 years, continues to affect current and conflicting interests of waterfront property owners and the general public. See, e.g., Ebbert, Bidden Shorelines, Boston Globe, June 25, 2006.
See, e.g., Storer v. Freeman, 6 Mass. 435, 439 (1810) (referring to the “margin of the sea, in its usual and ordinary state”); Sparhawk v. Bullard, 1 Met. 95, 108 (1840) (employing “low-water mark at such times when the tides ebb the lowest”); East Boston Co. v. Commonwealth, 203 Mass. 68, 70, 72 (1909) (attempting to distinguish between “the present line of mean low water, or to some other line of mean low water,” and stating that an order emanating from the General Court in 1640 that referred to “ordinary” low water “suggest[s] at once a distinction between the line indicated and absolute low water mark, or extreme low water mark”).
To which we might add, among other factors, seismic disturbances and changes in climate.
While “ mean” is not always synonymous with “average,” it is used interchangeably in this context. See Rockwood. v. Snow Inn Corp., 409 Mass. at 363 (defining “mean low water mark” as “a line established by an average of the low tides”). Thus the Spillanes’ argument is perfectly logical, akin to asserting that the average height of a group of persons need not correspond to the actual height of any person in the group.
The use of the NGVD in Houghton was not an issue on appeal. We noted *390that “[n]one of the parties . . . complains about [the judge’s] determination, based upon his consideration of precedent, scholarly articles, and the testimony of an expert, that the ‘high water mark’ and ‘low water mark’ were to be measured in accordance with the objective, relevant, standardized, and publicly available data compiled from survey stations established by the Federal government and located throughout the country, that is, National Geodetic Vertical Datum (NGVD).” Houghton v. Johnson, 71 Mass. App. at 829.
Mean water level (usually expressed as “mean lower low water”) is the tidal datum displayed on charts of the east, west and gulf coasts as well as the coasts of Alaska, Hawaii, the West Indies and other United States and United Nations Islands of the Pacific. United States Coast Pilot, Atlantic Coast (39th ed. 2009).
We note that the mean water levels measured by the NGVD will reflect average changes (“accretion” and “reliction”) over time; additionally we do not intend to preclude the use of other reliable and predictable techniques made possible by scientific advances in the future.
The Spillanes link ownership through their chain of title; the town makes the connection through the 1640 grant. The result, however, is the same.
Court: “I’m going to ask you, in terms of the town’s claim, to the extent there’s a claim of ownership here or the evidence by which you would contest plaintiffs’ claim to the flats, is it by way of taking?”
Town counsel: “No .... Just to clarify for the record, we’re not making an affirmative claim for ownership, but simply offering rebuttal evidence to [plaintiffs’] claim” (emphasis supplied).
The town did not formally assert an affirmative claim to quiet title until August 3, 2007, the final day of trial.