OPINION
Before RABINOWITZ, C. J., CONNOR and BOOCHEVER, JJ., and DIMOND, J. Pro Tern. CONNOR, Justice.This case raises legal and factual questions concerning the law of accretion in Alaska. Fred and Helen Pankratz have brought an appeal seeking costs and attorney’s fees following a quiet-title judgment rendered in their favor by the superior court. The State of Alaska has cross-appealed, claiming that the trial court erred in finding that the property, located on the Chena River near Fairbanks, has accreted to the legal benefit of appellants.
I.
In 1961 appellants purchased a parcel of land on the banks of the Chena River. An island, which is now known as “Pike’s Island”, lies in the middle of the river, in front of the property which the Pankratzes acquired in 1961. In 1965, Mr. Lloyd Pike obtained title to the island through a patent from the federal government; hence the name, Pike’s Island. On May 7, 1969, Fred Pankratz acquired Pike’s Island from Lloyd Pike.
In August of 1967 the Chena River experienced an unusually severe flood. Following that flood, aerial photographs revealed that the southeast channel of the river, which is located between the Pank-ratzes’ mainland parcel and Pike’s Island, was either not flowing at all, or was very shallow.
On Ocotober 30, 1968, the State of Alaska, through its Division of Lands, entered into the first of two gravel bailing con*987tracts with Fred Pankratz. This contract of sale authorized Pankratz to bail gravel from the southeast bed of the Chena River, slightly upstream from Pike’s Island. The first contract expired on August 1, 1969.
By April 29, 1969, Pankratz had undertaken substantial bailing operations in the Pike’s Island area of the Chena River. It is apparent that a gravel bar was beginning to emerge from the river, directly contiguous to the upstream end of Pike’s Island. This gravel bar constitutes the disputed property in this lawsuit.
On October 8, 1969, Pankratz and the State entered into a second gravel bailing contract. This agreement called for Pank-ratz to bail along two fifty foot long “removal zones” on the far side of the gravel bar.
By the early summer of 1970, Pankratz had stockpiled a large quantity of bailed gravel on the bar which was continuing to emerge along the upstream end of Pike’s Island. The second contract expired on July 29, 1970.
Beginning on June 19, 1970, the State wrote to Pankratz demanding that he remove the stockpiled gravel from the emerging bar, which the State claimed to own. Similar demands were made on July 24, 1970, and August 4, 1970. Pankratz did not remove the gravel. A letter dated November 16, 1970, suggested that a lawsuit was imminent if the matter was not resolved quickly.
On May 21, 1971, the State filed a four-count lawsuit against Fred and Helen Pankratz. The complaint sought, inter alia, to have the Pankratzes restore the southeast river channel and end their trespass on the bar, to have the bailed gravel removed from the gravel bar, and to have title to the bar quieted in the State’s name. The Pankratzes counterclaimed, asking that title be quieted in their names and that the State be ordered to issue yet a third gravel sale contract to them.
In April of 1973, the case was tried by the superior court, without a jury. On October 23, 1973, the court issued a memorandum decision awarding title to the bar to the Pankratzes. All other claims or counterclaims have either been settled or were denied. From that decision the Pankratzes have appealed, claiming costs and attorney’s fees. The State cross-appealed, claiming that the court erred in quieting title to the bar in favor of the Pankratzes.
On appeal we are confronted with three claims of error. In its cross-appeal the State argues that the court erred in finding that the gravel bar had emerged above the annual mean high-water mark of the Chena River. It further argues that the judge erred in finding that the Pankratzes did not cause the gravel bar accretion to occur. The Pankratzes, in their appeal, argue that Judge Gilbert’s failure to award costs and attorney’s fees to them, without explanation, constitutes error under the “prevailing party” doctrine of Alaska Civil Rule 82(a).1
II.
Both of the errors claimed by the State are related to the question of whether there was sufficient evidence to support Judge Gilbert’s findings that the gravel bar had accreted above the mean high-water mark and that the Pankratzes had not caused that accretion by their own conduct. Before we will reverse the trial court’s findings in judge-tried cases, we must have a definite and firm conviction that error was committed.2
*988At the outset it is useful to review the law of accretion in cases such as this. Normally, in private litigation involving land, state law, rather than federal law, provides the substantive rules.3 However, in the present controversy Fred Pankratz has traced his title to Pike’s Island back to a federal patent which was granted to Lloyd Pike in 1965. In Borax Consolidated, Ltd. v. City of Los Angeles, 296 U.S. 10, 22, 56 S.Ct. 23, 29, 80 L.Ed. 9 (1935), the Supreme Court held:
“The question as to the extent of this federal grant, that is, as to the limit of the land conveyed, ... is necessarily a federal question. . . . [I]t involves the ascertainment of the essential basis of a right asserted under federal law.” (emphasis added)
This rationale for applying federal law in cases involving federal patents was first used in an accretion case in Hughes v. Washington, 389 U.S. 290, 290-92, 88 S. Ct. 438, 19 L.Ed.2d 530 (1967). In Bonel-li Cattle Co. v. Arizona, 414 U.S. 313, 94 S.Ct.'517, 38 L.Ed.2d 526 (1973), federal law was applied to an accretion case involving a navigable river. The present case concerns a claim of accretion to an island granted by a federal patent on a navigable stream. We therefore conclude that federal law, rather than state law, controls the substantive issues presented herein.
Both sides agree that the State has title to the bed of its navigable rivers, such as the Chena River, up to the ordinary high-water mark, as modified by accretion. In Bonelli Cattle Co. v. Arizona, supra, the United States Supreme Court explained that the states claim title to the navigable river beds within their borders under the so-called “equal-footing” doctrine,4 which Congress in effect codified when it quit-claimed federal interests to such lands in 1953.5 But the court held in Bonelli that neither the equal-footing doctrine nor the Submerged Lands Act of 1953 permitted the application of state law in a controversy between a private landowner and the state over title to accreted land on a navigable stream.
The meaning of the “ordinary high-water mark” under federal law is somewhat unclear. While such a boundary line can often be traced by the eye without difficulty,6 a definition of the phrase is useful when a bona fide dispute arises.
In Oklahoma v. Texas, 260 U.S. 606, 625-40, 43 S.Ct. 221, 67 L.Ed. 428 (1923), the Supreme Court held that the high-water mark is coterminous with the outer limit of the “bed” of the river. The Court defined the bed of the river as land which is “kept practically bare of vegetation by the wash of the waters of the river from year to year, in their onward course, although parts of it are left dry for months at a time . . . .” Oklahoma v. Texas, supra at 632, 43 S.Ct. at 225. In United States v. Claridge, 279 F.Supp. 87, 91 (D. C.Ariz.1967), affd, 416 F.2d 933, 934 (9th Cir. 1969), cert, denied, 397 U.S. 961, 90 S.Ct. 994, 25 L.Ed.2d 253 (1970), the court stated:
“The ordinary high water mark of a river is a natural physical characteristic *989placed upon the lands by the action of the river. It is placed there, as the name implies, from the ordinary flow of the river and does not extend to peak flow or flood stage so as to include overflow on the flood plain, nor is it confined to the lowest stages of the river flow.” (footnote omitted)
The relevance and method of ascertaining the ordinary high-water mark was definitively explained in Borough of Ford City v. United States, 345 F.2d 645, 648-51 (3rd Cir. 1965), cert, denied, 382 U.S. 902, 86 S.Ct. 236, 15 L.Ed.2d 156 (1965). In that case the court noted that the demarcation of boundaries along navigable streams is generally readily observable. The court went on to explain that the high-water mark usually can be detected by observing the presence of multiple factors, including shelving, a change in the character of the soil, the absence of litter, and the destruction of terrestrial vegetation. When the multiple factors comprising a high-water mark cannot be found in one location, it is permissible to check for them at other sites along the stream.
If these multiple phenomena cannot be found, resort to the so-called “vegetation test” alone is appropriate.’7' Under these circumstances the high-water mark rests at the point below which the value of the soil for agricultural purposes has been destroyed.8 This does not mean that all vegetation is absent below the mark,9 but rather that terrestrial vegetation will not grow there.10
In Bonelli Cattle Co. v. Arizona, 414 U. S. 313, 325, 94 S.Ct. 517, 526, 38 L.Ed.2d 526 (1973), the Supreme Court stated:
“federal law recognizes the doctrine of accretion whereby the ‘grantee of land bounded by a body of navigable water acquires a right to any . . . gradual accretion formed along the shore.’ When there is a gradual and imperceptible accumulation of land on a navigable riverbank, by way of alluvion or reliction, the riparian owner is the beneficiary of title to the surfaced land . . . .” (citations omitted)
Fred and Helen Pankratz claim to be the beneficiaries of such accretion in the form of the gravel bar which has emerged along the upstream end of Pike’s Island.
It is well established that the burden of proving accretion rests with the party claiming the benefit thereof. Oklahoma v. Texas, 260 U.S. 606, 638, 43 S.Ct. 221, 67 L.Ed. 428 (1923). Alaska state law is in accord. Schafer v. Schnabel, 494 P. 2d 802, 807 (Alaska 1972).
It is likewise settled that accretion may result from artificial causes, provided that the party claiming the benefit did not himself cause the artificial accumulation. Bonelli Cattle Co. v. Arizona, 414 U.S. 313, 327, 94 S.Ct. 517, 38 L.Ed.2d 526 (1973); United States v. Claridge, 416 F.2d 933, 935 (9th Cir. 1969). Alaska state law is again in accord. Schafer v. Schnabel, 494 P.2d 802, 807 (Alaska 1972).
III.
With these legal principles in mind, we now turn to a review of the record in this case.
At trial, the Pankratzes called as an expert witness Mr. Leslie R. Rogers, a professional surveyor. Mr. Rogers presented *990a diagram which purported to establish the ordinary mean high-water mark in the vicinity of Pike’s Island. The diagram indicates that the gravel bar at the head of Pike’s Island is above the mark.
Mr. Rogers testified about the manner in which the chart had been constructed. He states that he had selected four sites on the far bank of the Chena River.11 Two of the sites were above Pike’s Island, and two were below the island. In each spot, substantial terrestrial vegetation was present. He then took elevation readings at each of these locations, and these readings were then plotted on the diagram. Connecting lines were drawn and the chart was submitted into evidence as indicative of the location of the ordinary mean high-water mark. Mr. Rogers testified that the gravel bar had accreted above the ordinary mean high-water mark.
The State argues that the evidence presented by the Pankratzes is insufficient to support a finding that the gravel bar had accreted above the mean high-water mark. In this regard the State appears to rely on the testimony of two witnesses, plus an evidentiary presumption which may be relevant in cases involving the location of ordinary high-water marks.
The State called Mr. Enzo Becia as an expert in photographic interpretation. Mr. Becia imposed “vegetation” lines on aerial photographs of the disputed territory. Although these lines might reflect an eleva-tional variance from the ordinary high-water mark constructed on Mr. Rogers chart, Mr. Becia’s perceptual abilities were severely impeached on cross-examination.
The State also called Dr. Charles Behlke, who has a doctorate in hydraulics. Doctor Behlke’s testimony centered on aerial photographs of Pike’s Island and certain U.S. Geological Survey records which revealed the rate at which the Chena River flowed when it passed a measuring station a few miles upstream from Pike’s Island. Apparently Dr. Behlke’s testimony was intended to establish an approximate location of the mean high-water mark, to within one foot above or below its actual location.
However, Dr. Behlke admitted that the U.S. Geological Survey records could not be used to determine where the actual mark in a particular place on the river was located. And he further admitted that at Pike’s Island the level of the Chena River would be affected by “backwater” from the Tanana River, into which the Chena flows a few miles downstream. Judge Gilbert sustained an objection to Dr. Behlke’s opinion as to the level of the high-water mark at Pike’s Island, on the grounds that the backwater from the Tanana created an unexplained variable which rendered the opinion useless.
Additionally, the State relies on the presumption created by us in Hawkins v. Alaska Freight Lines, 410 P.2d 992, 994 (Alaska 1966). In Hawkins, we held that where one party, by his own actions, has rendered determination of the high-water mark “impracticable,” the straight-line approximation called the “meander line” will be presumed to be the mark.12 The State contends that because Pankratz obliterated the high-water around Pike’s Island and the contested gravel bar, the Pankratzes’ *991proof must overcome the presumption created in the Hawkins case.
Our review of the record does not convince us that the appellants rendered a determination of the high-water mark impracticable. The State introduced photos of a bulldozer stripping the overburden on Pike’s Island, and drew admissions from Pankratz and his agent, George Horner, that they had stripped vegetation from Pike’s Island. But at no time did the State introduce any evidence proving that Pank-ratz’s conduct made determination of the high-water mark on the gravel bar impracticable.
Even if the presumption were operative, the State still has failed to offer sufficient proof to overcome the showing which the Pankratzes made at trial. In Rollins v. Leibold, 512 P.2d 937, 943-44 (Alaska 1973), we stated the following with regard to the effect of presumptions:
“[0]nce the presumption is established the opposing party has the burden of proving that the nonexistence of the presumed fact is more probable than its existence.”
In Cooksey v. State, 524 P.2d 1251, 1258 n.16 (Alaska 1974), we added,
“The rule merits adoption in cases tried by the court without a jury as well as those tried by a jury. In any event, the presumption once established can be dispelled by contrary evidence; the trier of fact must resolve the issue with the rule simply as a guide.” (emphasis added)
The Pankratzes offered direct proof of the high-water mark through expert testimony. The State failed to seriously impeach that testimony, and offered no credible conflicting evidence of its own. The trial judge found that the Pankratzes’ evidence was persuasive and ruled accordingly. Our review of the record shows nothing even approaching clear error in that ruling.
The State argues that if the gravel bar has accreted above the ordinary high-water mark, the Pankratzes, or their agents, caused the accretion to occur. Therefore, the Pankratzes cannot claim title to the property under the accretion doctrine. But, as mentioned above, it is settled that accretion may result from artificial causes, provided that the party claiming the benefit did not cause the artificial accumulation. Bonelli Cattle Co. v. Arizona, 414 U.S. 313, 327, 94 S.Ct. 517, 38 L. Ed.2d 526 (1973); United States v. Clar-idge, 416 F.2d 933, 935 (9th Cir. 1969); Schafer v. Schnabel, 494 P.2d 802, 807 (Alaska 1972).
To prove that the Pankratzes caused the accretion to occur, the State first attempted to show that the 1967 flood itself did not change the level of the ordinary high-water mark. The State relied on the testimony of Mr. Enzo Becia, who attempted to establish this proposition by drawing “vegetation lines” on aerial photographs taken before and after the flood. However, as noted earlier, Mr. Becia’s testimony was impeached by a showing that his perceptual skills were not particularly reliable. Even if Mr. Becia’s testimony were wholly credible, it would not establish that the Pank-ratzes’ conduct caused the accretion, but simply that the flood did not cause the buildup.
On the question of causation, the State points to testimony tending to show that the Pankratzes had bailed the area before the first contract was signed on October 30, 1968. The State also points to evidence showing that under the first contract, Pankratz clearly bailed in the wrong place, stockpiled the gravel so as to impair the flow in the southeast channel, and bailed after the first contract expired, but before the second contract was signed.
The Pankratzes countered all of this with numerous witnesses, most of whom were not shown to have any interest in the case. They testified to two facts. First, the'bar had not “grown” larger in recent memory. Second, the southeast channel was usually dry and only filled during flooding, which could still happen after *992Pankratz began dredging. Thus, on the causal effect of Pankratz’s activity, the evidence is conflicting. We hold that Judge Gilbert did not commit clear error in finding that the Pankratzes did not cause artificial accretion.13
IV.
Since we find no clear error in the judgment to quiet title to the gravel bar in the Pankratzes’ favor, we must decide whether the court erred in refusing to award them costs and attorney’s fees.
There is no doubt that the Pankratzes are the prevailing parties. See De Witt v. Liberty Leasing Co., 499 P.2d 599, 600-01 (Alaska 1972); Buza v. Columbia Lumber Co., 395 P.2d 511, 514 (Alaska 1964). They succeeded on the main issue in the lawsuit, which was the ownership of the Pike’s Island bar.
' The Pankratzes rest their “abuse of discretion” claim on four separate assertions. First, they claim that the suit filed by the State was reckless litigation. There is nothing to support this assertion.
Second, they claim that the State “abandoned” most of the counts as the trial progressed. The complaint was in four counts seeking to quiet title to the bar in the State’s name and to have the Pank-ratzes remove the gravel from the bar, end their trespass on the bar, and unblock the southeast channel. The validity of the last three points hinged largely on the quiet-title action. It was perhaps prudent trial strategy to focus on the quiet-title aspects of the case.
The third argument on which the Pankratzes rely is that the State presented “very little evidence” in support of its claim. This is simply not the case. The State presented dozens of exhibits and testimony amounting to about half the entire transcript during its case in chief. A party should not be assessed costs and fees merely because the evidence offered was not persuasive.
Finally, however, the Pankratzes claim that the trial judge abused his discretion by failing to state any reason for his denial of the claim. In Cooper v. Carlson, 511 P.2d 1305 (Alaska 1973), we discussed this precise issue. There, the plaintiff, a lessor, sued his lessee for taking gravel from leased land. The lessee prevailed generally but was denied costs and fees without explanation. He appealed and we remanded the case, since we could not determine whether the trial court had denied the claim because it thought appellant was not the prevailing party or simply as an exercise of its discretion.
In the present case the trial judge found that the Pankratzes prevailed on the “principal issue” at bar. Nevertheless, he held that each party should bear its own costs and attorney’s fees, and he did not explain why his ruling deviated from the general rule that costs and attorney’s fees are normally awarded to the prevailing party.14
Under Cooper v. Carlson, supra, we will remand the case to Judge Gilbert, sitting pro tempore, for the purpose of determining whether costs and attorney’s fees should be denied in his discretion, in which event the reasons for exercising such discretion should be set forth.
The judgment below is affirmed with regard to the Pankratzes’ title to the property. The case is remanded on the question of awarding costs and attorney’s fees to appellants.
Affirmed in part, remanded in part.
*993ERWIN and FITZGERALD, JJ., not participating.. Alaska Civil Rule 82(a) provides in perti-net part:
“(a) Allowance to Prevailing Party as Costs.
(2) In actions where the money judgment is not an accurate criteria for determining the fee to be allowed to the prevailing side, the court shall award a fee commensurate with the amount and value of legal services rendered.”
. See, e. g., Fiche v. Alaska Airlines, Inc., 624 P.2d 271, 274 (Alaska 1974); Alaska Foods, Inc. v. American Manufacturer’s Mutual Insurance Co., 482 P.2d 842, 848 (Alaska 1971).
. H. M. Hart & H. Weschsler, The Federal Courts and the Federal System 776-77 (2nd ed. 1973).
. “When the original colonies ratified the Constitution, they succeeded to the Crown’s title and interest in the beds of navigable waters within their respective borders. . As new States were forged out of the federal territories after the formation of the Union, they were ‘admitted [with] the same rights, sovereignty and jurisdiction ... as the original States possess within their respective borders.’ Accordingly, title to lands beneath navigable waters passed from the Federal Government to the new States, upon their admission to the Union, under the equal-footing doctrine.” (footnotes omitted) Bonelli Cattle Co. v. Arizona, 414 U.S. 313, 317-18, 94 S.Ct. 517, 522 (1973).
. See Bonelli Cattle Co. v. Arizona, 414 U.S. 313, 319, 94 S.Ct. 517, 38 L.Ed.2d 526 (1973) ; Submerged Lands Act of 1953, 43 U.S.C. § 1301 et seq.
. Oklahoma v. Texas, 260 U.S. 606, 629, 43 S.Ct. 221, 67 L.Ed. 428 (1923).
. See Borough of Ford City v. United States, 345 F.2d 645, 648 (3rd Cir. 1965), cert, denied, 382 U.S. 902, 86 S.Ct. 236, 15 L.Ed.2d 156 (1965).
. See Howard v. Ingersoll, 54 U.S. (13 How.) 381, 415, 14 L.Ed. 189 (1851) ; Borough of Ford City v. United States, 345 F.2d 645, 648 (3rd Cir. 1965), cert, denied, 382 U.S. 902, 86 S.Ct. 236, 15 L.Ed.2d 156 (1965).
. But see United States v. Chicago, B. é Q. R. Co., 90 F.2d 161, 170 (7th Cir. 1937), cert, denied, 302 U.S. 714, 58 S.Ct. 33, 82 L.Ed. 551 (1937).
. See Borough of Ford City v. United States, 345 F.2d 645, 648 (3rd Cir. 1965), cert, denied, 382 U.S. 902, 86 S.Ct. 236, 15 L.Ed. 2d 156 (1965).
. Apparently, human activity in and around the gravel bar led him to believe that he could take a better survey by selecting sites not directly on the disputed property.
. Federal law clearly establishes that the “meander line” normally does not constitute the high water mark. See, e. g., Niles v. Cedar Point Club, 175 U.S. 300, 308, 20 S.Ct. 124, 44 L.Ed. 171 (1899) ; Some v. Smith, 159 U.S. 40, 42-43, 15 S.Ct. 988, 40 L.Ed. 68 (1895) ; Shively v. Bowlby, 152 U.S. 1, 39, 14 S.Ct. 548, 38 L.E'd. 331 (1894) ; Nordale v. Wasoberg, 84 F.Supp. 1004, 1006, 12 Alaska 399 (D.Alaska 1949). However, the presumption announced in the Hawkins opinion is a procedural rule, adopted to facilitate the establishment of a hard-to-prove fact. For this reason, the presumption is available, even in a case controlled by federal substantive law.
. The State devotes about four pages of its cross-appeal brief to the contention that the Pankratzes materially breached the second bailing contract. Apparently, this section is designed to demonstrate that the Pankratzes alleged artificial alterations were not at the State’s behest. However, since the State has failed to establish clear error on the issue of causation, this point is moot.
. See R.Civ.P. 82, footnote 1 supra.