The Watershed Management Act, G. L. c. 92Aih, §§ 1-20 (Act), is designed to protect certain water systems that are critical to the public water supply. The plaintiffs1 own lakefront property located within a 200-foot buffer zone created by the Act for land abutting particular sources of drinking water. Pursuant to G. L. c. 92Alh, § 5, alterations within that buffer zone are prohibited unless a variance is issued. The plaintiffs’ single-family home is located on the property. To increase the size of their lawn and double the extent of their existing sandy beach, the plaintiffs sought a variance to remove trees from a forested area of their property. The Department of Conservation and Recreation (department) denied the variance on the ground that the proposed alterations would be harmful to the water supply; the department determined that the trees in their natural state would better protect water quality than would a lawn and beach.

The plaintiffs sought judicial review, asserting that the denial of the variance was a regulatory taking of a portion of their property, and that they were entitled to compensation by art. 10 of the Massachusetts Declaration of Rights2 and art. 49 of the Amendments to the Massachusetts Constitution, as amended by *636art. 97 of the Amendments (art. 49).3,4 Because we decline to adopt the plaintiffs’ argument that, for the purposes of a regulatory taking, the “relevant parcel” is the affected portion of the property, rather than the entire parcel, we agree with the determination of the Superior Court that the denial of the variance did not constitute a regulatory taking and affirm the judgment.5,6

1. Background and prior proceedings. The essential facts are not disputed. In 1977, the plaintiffs purchased a 2.87 acre parcel on Demond Pond in Rutland.7 Demond Pond is deemed a “great pond” protected under G. L. c. 92A1/2, § 1; it drains into the Ware River, which intermittently enters the Quabbin Reservoir.8 When the plaintiffs purchased the property, it was largely forested but contained a small vacation cottage and a sixty-foot sandy beach. In 1994, the plaintiffs received a building permit from *637the town of Rutland (town) to demolish the cottage and construct a year-round single-family home with a detached three-car garage; they occupy this home for “several months” each year. These modifications conformed with the provisions of G. L. c. 92AlA, § 5 (h), which explicitly permit construction of a single-family home on any lot existing prior to July 1, 1992 (the effective date of the Act).

In 1997, the plaintiffs further modified a portion of the property within the buffer zone. They cut down trees; extended the lawn by 6,000 square feet; excavated topsoil along the shoreline and imported sand to lengthen the beach by sixty feet (8,000 square feet); installed an eighty-foot long by thirty-inch high retaining wall; and built a three-foot wide brick path across the lawn to the beach. Although the plaintiffs obtained a building permit from the town to make these enhancements, they did not seek a variance from the department.

Pursuant to G. L. c. 92A1A, § 8, the department instituted enforcement proceedings, alleging that, by making the modifications without obtaining a variance, the plaintiffs had violated the terms of G. L. c. 92A1 A, § 5. A Superior Court judge rejected the plaintiffs’ takings claim, determined that the plaintiffs had violated the Act, and ordered the property restored to the condition that it was in prior to the 1997 modifications. The plaintiffs appealed and the Appeals Court determined that, since the plaintiffs had not applied for and been denied a variance, their claims were not ripe for review. See Commonwealth v. Blair, 60 Mass. App. Ct. 741, 749 (2004).

The plaintiffs then entered into an agreement with the department whereby they removed portions of the beach and the retaining wall and replanted their property in accordance with the department’s requirements. They applied subsequently for a variance to restore the improvements that had been removed pursuant to the agreement with the department. The department denied that application and the plaintiffs again sought review in the Superior Court, claiming that the denial of the variance constituted an unconstitutional taking without compensation in violation of art. 10 and art. 49. A second Superior Court judge denied the plaintiffs’ claims and the plaintiffs appealed to the Appeals Court. We transferred the case on our own motion.

*6382. Provisions of the Act. The Act was designed to protect designated reservoirs and their tributaries (the “watershed system”), including the Quabbin Reservoir, in order to provide a clean public water supply. See G. L. c. 92 A1 k, § 1. The Act prohibits “alterations” within 200 feet of the banks of waters within the watershed system, and limits certain types of development within 400 feet of those banks. See G. L. c. 92A1 k, §§ 1, 5; 350 Code Mass. Regs. §§ 11.00 et seq. (1994). As applicable here, “alterations” are defined to include “draining, dumping, dredging, damming, discharging, excavating, filling or grading; . . . [and] the changing of run-off characteristics.” G. L. c. 92Alk, § 1. However, such alterations may be permitted if a variance is obtained. See G. L. c. 92Alk, § 5 (/). The Act authorizes the department, on behalf of the Commonwealth, to “take by eminent domain . . . , or acquire by purchase or otherwise, lands in fee, easements, rights and other property that it deems necessary or desirable for carrying out the powers and duties [conferred upon it by the Act].” See G. L. c. 92AV2, § 17.

3. Takings claims. The plaintiffs argue that the Act is facially invalid under both art. 10 and art. 49, because it grants the department a de facto property interest in their real estate without compensation. Thus, they urge us to declare the Act unconstitutional on its face. In addition, the plaintiffs contend that provisions of the Act, as applied to them through the denial of the variance, represent a taking without compensation. The plaintiffs assert that the denial of the variance was a physical taking because it granted an easement or the equivalent of an easement to the department, including the right to enter onto the property. They claim further that we should interpret art. 10 (requiring that “no part of the property of any individual” may be taken without compensation) to provide more expansive protection than the just compensation clause of the Fifth Amendment to the United States Constitution (“nor shall private property be taken for public use, without just compensation”), and that, under this more expansive reading, the denial of their application for a variance was a regulatory taking without compensation and was thus unconstitutional.

a. Facial invalidity. The plaintiffs claim that the Act is facially unconstitutional because it grants the equivalent of an easement *639to the department without compensation. We presume that statutes are constitutional; a plaintiff making a facial challenge to a statute faces a heavy burden to prove otherwise. See Blixt v. Blixt, 437 Mass. 649, 652 (2002). See also Sturges v. Chil-mark, 380 Mass. 246, 256 (1980). The plaintiffs fail to satisfy that burden.

A statute does not, on its face, effect an unconstitutional taking when there are any circumstances in which an owner retains an economically viable use of his or her property. See Hodel v. Virginia Surface Mining & Reclamation Ass’n, 452 U.S. 264, 295-297 (1981). The Act provides a variance procedure pursuant to which landowners may seek exemption from the prohibition on building in the buffer zone. G. L. c. 92AV2, § 5 (/)■ In addition, the Act sets forth a number of explicit exceptions, among them uses lawfully existing prior to July 1, 1992, and the construction of a new single-family home on any lot existing prior to July 1, 1992. See G. L. c. 92Alh, § 5 (c), (h). Moreover, the Act authorizes the department to take by eminent domain, see G. L. c. 92AV2, § 17, necessarily invoking the right to obtain compensation pursuant to G. L. c. 79, § 10.

Because the Act includes explicit exceptions as well as a variance procedure, the Act does not, on its face, establish an interest in land without compensation under every possible circumstance. See Hodel v. Virginia Surface Mining & Reclamation Ass’n, supra. See also Gilbert v. Cambridge, 932 F.2d 51, 64 (1st Cir. 1991). Therefore, the Act is not facially invalid and we turn to the plaintiffs’ as applied claims.

b. Physical taking. A physical or per se taking necessitating compensation under the Fifth Amendment requires a permanent physical intrusion on, or outright acquisition of, an interest in the property by the government for public use. See Yee v. Escondido, 503 U.S. 519, 522 (1992); Philip Morris, Inc. v. Reilly, 312 F.3d 24, 33 (1st Cir. 2002). See discussion in Tahoe-Sierra Preservation Council, Inc. v. Tahoe Regional Planning Agency, 535 U.S. 302, 321-326 (2002) (.Lake Tahoe), and cases cited. A physical taking comes about when there is a permanent intrusion even on a very small piece of the property, notwithstanding that the owners retain title to that portion. See Loretto v. Teleprompter Manhattan CATV Corp., 458 U.S. 419,426-437 (1982).

*640The plaintiffs contend that enactment of the Act, and the denial of their application for a variance due to the buffer zone restrictions established by the Act, essentially conveys the equivalent of an easement on their property to the department, without compensation, in violation of art. 49.9 See Cann v. Commonwealth, 353 Mass. 71, 74-75 (1967) (restricting access to public way as result of highway ramp construction granted easement to Commonwealth requiring compensation); Inhabitants of Watertown v. Dana, 255 Mass. 67, 70 (1926) (building line [setback] “is in the nature of an easement for the benefit of the public” and operates as taking of private property for public use under power of eminent domain). This argument fails. The Act does not grant the department or any other agency or person a right to use the plaintiffs’ land, or to derive a benefit from the property, as would be required to create an easement. See Commercial Wharf E. Condominium Ass ’n v. Waterfront Parking Corp., 407 Mass. 123, 133 (1990) (defining easement as “an interest in land which grants to one person the right to use or enjoy land owned by another”). See also Ritger v. Parker, 8 Cush. 145, 147 (1851). It simply restricts the uses that the plaintiffs may make of a portion of that land. The plaintiffs retain the right to use their land, as a whole, and retain the exclusive right to control access to the forested portion adjacent to the pond. The Act merely regulates the use of certain portions of the land abutting the public watershed. See Sturges v. Chilmark, supra at 253, 256.

The plaintiffs point out, correctly, that the Act authorizes the department to purchase property to further its purposes. The Act does not, however, require that such purchases be made. Furthermore, art. 49 provides that enjoyment of the land, air, water, and “natural, scenic, historic, and esthetic qualities of [the] environment” are a “public purpose” and that compensation may be paid to allow the acquisition of land for this purpose; it does not require the acquisition of private property, nor does it provide a separate right to compensation for the enforcement of land use *641regulations. In this case, since no easement was created by the Act or by the denial of the variance application, no compensation is required under art. 49.

c. Regulatory takings. In addition to their per se takings claims, the plaintiffs argue that the denial of their application for a variance constitutes a regulatory taking. A regulatory taking, a concept adopted by the United States Supreme Court for the first time in 1922, arises not from the acquisition of an interest in property by the government, but rather from a regulation enacted under the State’s police power that severely limits the property’s use.10 See Pennsylvania Coal Co. v. Mahon, 260 U.S. 393, 415 (1922). While most restrictions on the use of private property do not constitute a taking, when a regulation substantially restricts the owner’s use of the property, so that the regulation “goes too far,” it may be deemed a regulatory taking of that property for a public use. See id. Whether a regulation “goes too far” is determined ordinarily by a three-prong test. See Penn Cent. Transp. Co. v. New York City, 438 U.S. 104, 124-125 (1978) (Penn Central). Thus, courts consider (1) “the economic impact of the regulation on the claimant”; (2) “the extent to which the regulation has interfered with distinct investment-backed expectations”; and (3) “the character of the governmental action.” Leonard v. Brimfield, 423 Mass. 152, 154, cert, denied, 519 U.S. 1028 (1996), quoting Connolly v. Pension Benefit Guar. Corp., 475 U.S. 211, 225 (1986). See Lopes v. Peabody, 417 Mass. 299, 304 (1994).

Additionally, in limited circumstances, a regulatory taking may be deemed a “categorical taking.” A “categorical taking” arises where a regulation is such that the owner retains no viable economic use of the property. See Lucas v. South Carolina Coastal Council, 505 U.S. 1003, 1015-1016 (1992) (Lucas); Lopes v. Peabody, supra at 304 n.9.11 If a regulation is determined not to impose a “categorical taking,” then the three-prong *642analysis of Penn Central, supra, is applied to determine whether the regulation nonetheless “goes too far.” See Lake Tahoe, supra at 320-327; Leonard v. Brimfield, supra at 154.

(i) Relevant parcel. To determine whether a regulatory taking has occurred, it is first necessary to decide the “relevant parcel” to which the regulation is applicable. See Giovanella v. Conservation Comm’n of Ashland, 447 Mass. 720, 726-731 (2006). Under the just compensation clause of the Fifth Amendment, which prohibits the taking of “private property ... for public use, without just compensation,” the “relevant parcel” has consistently been held to be the “parcel as a whole,” and whether a regulatory taking has occurred has been determined by considering the effect of a regulation as applied to an entire parcel. See Lake Tahoe, supra at 327. Treatment of the impact of a regulation on a portion of a parcel as a taking has been squarely rejected. See Penn Central, supra at 130-131 (“ ‘Taking’ jurisprudence does not divide a single parcel into discrete segments and attempt to determine whether rights in a particular segment have been entirely abrogated. In deciding whether a particular governmental action has effected a taking, this Court focuses rather both on the character of the action and on the nature and extent of the interference with rights in the parcel as a whole”). See also Moskow v. Commissioner of Envtl. Mgt., 384 Mass. 530, 533 & n.3 (1981).

To date, we have interpreted art. 10 consistently to provide property owners the same protection afforded under the just compensation clause of the Fifth Amendment. See, e.g., Daddario v. Cape Cod Comm’n, 425 Mass. 411, 415-418, cert, denied, 522 U.S. 1036 (1997); Lopes v. Peabody, supra at 304; Steinbergh v. Cambridge, 413 Mass. 736, 741-744 (1992), cert, denied, 508 U.S. 909 (1993). The plaintiffs ask us to decide that, contrary to our long-standing precedent, art. 10 is more expansive. The plaintiffs argue that the language “no part of the property of any individual” in art. 10 should be interpreted to define the “relevant parcel” under art. 10 more broadly than the “relevant parcel” under the Fifth Amendment. They contend that art. 10 applies to the taking of any part of a landowner’s property, and that, rather *643than the “parcel as a whole,” the “relevant parcel” under art. 10 may consist only of that part of the property affected by the regulation.12 Thus, the plaintiffs assert that the Act, as applied to them, is unconstitutional under art. 10 because it denies them all economically viable use of a portion of their property. We decline to adopt this interpretation, and conclude that the phrase “no part of the property of any individual,” in the context of a regulatory taking, does not refer to one portion of a single parcel of land.

The Massachusetts Declaration of Rights was adopted before the United States Constitution, when concepts such as zoning and regulatory takings had yet to emerge. At the time of its adoption, the taking of land referred to the government’s condemnation of land and the assumption of title to it. See Opinion of the Justices, 308 Mass. 619, 626 (1941); Callender v. Marsh, 1 Pick. 418, 429 (1823). See also Journal of the Convention for Framing a Constitution of Government for the State of Massachusetts Bay 36, 38, 225 (1832); Treanor, The Original Understanding of the Takings Clause and the Political Process, 95 Colum. L. Rev. 782, 790-791 (1995). The framers could not have intended the phrase “no part of the property of any individual” to refer to a regulatory taking, because regulatory takings were not recognized until 1922. Since the adoption of the Federal Constitution, we have consistently followed Federal takings analysis in considering the effect of a regulation only on an entire parcel. See Moskow v. Commissioner of Envtl. Mgt., supra at 533, and cases cited. See also Daddario v. Cape Cod Comm’n, supra at 415-417; Steinbergh v. Cambridge, supra at 741-744. We have been shown no reason to change that interpretation in this case.13

To adopt the interpretation proposed by the plaintiffs, and consider only that portion of a parcel affected by a regulation rather than the parcel as a whole, would upset the balance between *644protecting the public interest and protecting private property rights that is encompassed by the three-prong Penn Central test, and would elevate private property interests over public interests in virtually all circumstances. If the relevant parcel were considered to be only the portion of the property affected by the regulation, almost every valid land use or zoning regulation could be considered a “taking.” For instance, all zoning setbacks require that no building be constructed on certain portions of a parcel of land. See Pennsylvania Coal Co. v. Mahon, 260 U.S. 393, 413 (1922) (“Government could hardly go on if to some extent values incident to property could not be diminished without paying for every such change in the general law”). This interpretation would essentially prevent the implementation of land use regulations designed for the benefit of the citizens of the Commonwealth as a whole, such as the regulations here intended to provide clean water for this and future generations. See Gio-vanella v. Conservation Comm’n of Ashland, 447 Mass. 720, 726, 730 n.4 (2006).

The multifactor Penn Central balancing test provides property owners with an adequate remedy if a regulation does “go too far.” See Gove v. Zoning Bd. of Appeals of Chatham, 444 Mass. 754, 763-767 (2005). Because the test considers the effect of a regulation on the property as a whole, if a regulation deprives a plaintiff of a sufficiently substantial economic benefit that otherwise could have been derived from that property, application of the multifactor test may result in a determination that the regulation, as applied to that plaintiff, in fact requires compensation. See, e.g., Giovanella v. Conservation Comm’n of Ashland, supra at 733-735. We reject the plaintiffs’ contention that art. 10 affords greater protection than the Fifth Amendment in this context, and consider whether the denial of the variance in this case has brought about a regulatory taking of their entire parcel.

(ii) Application of regulatory takings analysis in this case. Notwithstanding the plaintiffs’ claims to the contrary, the denial of their application for a variance was plainly not a categorical taking. The plaintiffs retain title to the property and inhabit a single-family house on it. They concede, as they must, that they have not been deprived of all viable economic use of the property. Therefore, we consider whether the denial of the variance constituted a regulatory taking under the Penn Central analysis.

*645To determine the economic impact of the denial of the variance on the plaintiffs’ property, the first of the Penn Central factors, we consider the value of that property “before and after the alleged taking.” See Giovanella v. Conservation Comm’n of Ashland, supra at 725. The denial of the variance in this case imposes a permanent ban on any type of building or landscaping on approximately eight to eleven per cent of the plaintiffs’ property.14 This portion of the property, which was replanted according to the plaintiffs’ agreement with the department after the first round of litigation, must be allowed to revert to dense forest; thus, it does not accommodate camping, picnicking, sitting by the water, fishing, or other recreational activities. Contrast Lucas, supra at 1044 (Blackmun, J., dissenting) & 1065 n.3 (Stevens, J., dissenting) (although landowners could not build any structure on beachfront property, they retained some beneficial economic use because they could camp, picnic, fish, swim, and sunbathe on property). The department does not dispute that the plaintiffs retain no viable economic use of this portion of their property.

Nonetheless, the plaintiffs continue to derive significant economic benefit from their property as a whole. The property is zoned for single-family residential use. The plaintiffs have constructed a single-family house, a three-car detached garage, and a driveway on the locus; they retain also the use of the preexisting small sandy beach and dock. See Moskow v. Commissioner of Envtl. Mgt., supra at 533, citing Lovequist v. Conservation Comm’n of Dennis, 379 Mass. 7, 20 (1979). The eight to eleven per cent reduction in the amount of land that the plaintiffs can use may result in a diminution in value of their property,15 but it does not interfere with the plaintiffs’ use of the land to the extent that would represent a taking. We have determined previously that a wetlands regulation prohibiting building on fifty-five per cent of a plaintiff’s land, where that portion of the land retained no economically viable use but the plaintiff could build a single-family house on the remaining portion, did not constitute a taking. See Moskow v. Commissioner of Envtl. Mgt., supra at 531, 533 n.3.

*646Similarly, the denial of the variance does not interfere substantially with the plaintiffs’ investment-backed expectations. In Moskow v. Commissioner of Envtl. Mgt., supra, the landowners were unable to build on fifty-five per cent of a 297,000 square foot parcel that would otherwise have comprised at least eight house lots. See id. at 533 n.3. Here, in contrast, the plaintiffs have built a single-family house on a lot zoned for that purpose, and have been denied merely the ability to install a larger beach or lawn on eight per cent of their property. See Leonard v. Brimfield, 423 Mass. 152, 156, cert, denied, 519 U.S. 1028 (1996) (governmental action may preclude most beneficial use of property without constituting taking); Turnpike Realty Co. v. Dedham, 362 Mass. 221, 236-237 (1972), cert, denied, 409 U.S. 1108 (1973) (substantial diminution in value of property does not necessarily result in regulatory taking).

Finally, turning to the character of the governmental action, the plaintiffs do not dispute that the regulations implementing the provisions of the Act, see 350 Code Mass. Regs. §§ 11.00 et seq. (1994), pursuant to which the variance was denied, were adopted for the public purpose of ensuring a clean water supply under the State’s police power. See Moskow v. Commissioner of Envtl. Mgt., supra at 534-535, citing Penn Central, supra at 133. The requirement that a portion of the plaintiffs’ land be left in its natural state, to prevent pesticides and fertilizers from entering the public water supply, is the type of limited regulation designed to mitigate public harm from private use of land that does not require compensation. See Gove v. Zoning Bd. of Appeals of Chatham, 444 Mass. 754, 767 (2005). Therefore, there was no regulatory taking, and no compensation is required.16

Judgment affirmed.