
65 P.3d 876 (2003)
ANCHORAGE POLICE & FIRE RETIREMENT SYSTEM, Appellant,
v.
Jack GALLION, Michael Crotty, John Young, Carroll Grant, Anthony Provost, Douglas K. Bohac, and Anchorage Police and Fire Retirees Association, Appellees.
No. S-9880.
Supreme Court of Alaska.
March 14, 2003.
*877 Douglas J. Serdahely and David J. Mayberry, Patton Boggs LLP, Anchorage, for Appellant.
Peter J. Maassen, Ingaldson Maassen, P.C., and Peter Gruenstein, Gruenstein & Hickey, Anchorage, for Appellees.
Before: MATTHEWS, EASTAUGH, BRYNER, and CARPENETI, Justices.

OPINION
EASTAUGH, Justice.

I. INTRODUCTION
The superior court held the Board of Trustees of the Anchorage Police & Fire Retirement System in indirect criminal contempt for violating a court order that approved a class action settlement. Indirect criminal contempt requires finding beyond a reasonable doubt that the respondent violated an order willfully. Because the superior court found that the system willfully violated the court's order, because we conclude that the evidence supports that finding and that the order was unambiguous, and because we also conclude that there is no indication the superior court applied the wrong standard of proof, we affirm.

II. FACTS AND PROCEEDINGS
The Anchorage Police & Fire Retirement System (APFRS, or system) from 1994 to 1997 consisted of three benefit plans (Plans I, II, and III) that provided retirement, disability, and death benefits for Municipality of Anchorage police officers and fire fighters. At pertinent times the board of trustees administering the APFRS consisted of eight members.[1] The Anchorage mayor appointed the board's eight members; four were chosen from the mayor's administration and four were chosen from a list of persons nominated by the APFRS membership.[2]
*878 As of 1994 Plan I was 135% funded, Plan II was 112% funded, and Plan III was 89% funded; thus, Plans I and II were over-funded, Plan III was under-funded, and the three plans were over-funded in the aggregate.[3] In 1994 the Anchorage Assembly passed Anchorage Ordinance 94-95, combining the plans and requiring that the assets of Plans I and II fund Plan III.[4] APFRS members sued, challenging the constitutionality of the ordinance.[5] We held in Gallion v. Municipality of Anchorage (Gallion I) that the assets of the three plans could not be combined to fund all three plans to the detriment of the members of Plans I and II, and that the surpluses of each of those plans had to be used for the sole benefit of its members.[6]
Following our remand, APFRS members filed a second class action (Gallion II) in which they claimed that the APFRS board had not used the funds' surpluses for the benefit of the members in compliance with our decision in Gallion I. The members, represented by class counsel, sought to recover some of the monies by "either reduc[ing] contributions, increas[ing] benefits, or both." In March 2000 the class, the board, and the Municipality of Anchorage entered into a Conditional Settlement Agreement (CSA, or agreement) to settle Gallion I, Gallion II, and two other lawsuits.[7] Among other things, the CSA provided for distributing funds from the three plans to their respective members, provided for a one-time reversion of $40 million to the municipality, and provided for attorney's fees for class counsel.
Superior Court Judge John Reese conducted a hearing on March 17, 2000, approved the proposed CSA, and approved an award of attorney's fees to class counsel. The court observed that some class members had filed objections, some of which harshly criticized class counsel, to the proposed award of fees to class counsel. The court's oral comments explained at length the court's reasoning in rejecting those objections and in calculating the amount of its fee award to class counsel. The superior court entered a written order on April 6, 2000 awarding attorney's fees to class counsel. The April 6 order also ordered APFRS, when it distributed the funds to the members per the CSA, to send each member a copy of the court's written findings along with a copy of the transcript of the court's oral order. This requirement was intended to educate the members about the court's reasons for the fee award and was apparently intended to respond to members' criticism of class counsel. Thus, the April 6 order awarding attorney's fees provided:
[S]o that the APFRS members may fully understand the basis for the court's order with respect to attorneys' services and fees, it is further ORDERED that the APFRS shall mail at the expense of the common fund to each of the APFRS members a copy of these findings along with a copy of the transcript of the court's oral order no later than the date enhancements are distributed to retirees.

(Emphasis added.) The April 6 order therefore contemplated sending out copies of the transcript and findings at the same time, and no later than the time the system distributed the settlement payments to each APFRS member.
Several weeks later, the board filed a motion for clarification and interpretation of the CSA due to the board's professed concern about difficulties in making timely distributions.[8] In response, the superior court issued *879 a written order on April 28 that stated: "1. When sufficient funds have been made available through liquidation of investments to make all payments, all payments will be made. 2. Neither the Municipality nor the attorneys, nor the members, get paid before anyone else." The order also required that "5. The `educational' requirements of the settlement will be accomplished within the time allowed by the liquidation schedule. Distribution will not be delayed to accomplish education."
The system transferred money to class counsel, the municipality, and some class members on May 18, 2000. But there was a delay of about three weeks before the system distributed the court's findings regarding attorney's fees. The system first sent the transcript to members as an enclosure with a letter from the APFRS board dated June 8.[9] On June 9 the system filed a document entitled Notice of Compliance with Court Order; the notice stated that the required mail-out was completed June 7.
On June 21 class counsel moved for an order to show cause and for Rule 95 penalties; the motion asked court to sanction the board or its attorneys under Alaska Civil Rule 90(b) or Alaska Civil Rule 95. Following briefing, the court ordered the system and its counsel to appear and show cause why they should not be sanctioned "for violating the court's order concerning the timing of notification of the class members of the attorney fee dispute resolution."
After conducting an evidentiary hearing, the superior court found that "the distributions were made before the June 8th notice [enclosing the transcript] was sent." "[D]istributions were to the attorneys, the Municipality and 149 of the members.... I do find that that is contrary to the specific and unambiguous language of the April 6th order, so the system did violate that order, and in doing so defeated the purpose of that clause of the order." The court then held the system in contempt and announced an intention to fine it $100.[10] Counsel for the system argued that contempt required a willful violation of the order and that the evidence demonstrated that Charles Laird, who had acted for the board, "did not intentionally defy the court's order" and had an honest and good faith belief as to what he was required to do. The court nonetheless held the system in contempt. We discuss the court's comments in Part III.B of this opinion.
The court also found the system's attorney, Robert Klausner, in contempt and assessed, but suspended, a "nominal penalty" of $10 against him.
The APFRS appeals from the order holding the system in contempt. Klausner has not appealed.

III. DISCUSSION

A. Standard of Review
We review de novo a legal determination of what elements are necessary to prove indirect criminal contempt.[11] Relying by analogy on the standard of review applicable in deciding whether a court has made findings on each necessary element of a statutory violation,[12] we will review de novo contempt citations imposed under Alaska Civil *880 Rule 90(b).[13] We exercise our independent judgment in deciding whether a court has made factual findings satisfying each element necessary for indirect contempt. We review for clear error factual findings a court makes in deciding whether to hold a respondent in contempt.[14]
B. The Superior Court Found the Necessary Element of Willfulness When It Held the System in Indirect Criminal Contempt of Court.
The superior court held the system in contempt for disobeying the April 6 order.[15] This contempt was criminal because the sanction served a punitive, as opposed to a coercive, function.[16] The contempt was indirect because the court did not witness or hear the conduct constituting the contempt.[17]
The system argues that the superior court misdefined and misapplied the elements of indirect criminal contempt, because it omitted the requirement that the violation be willful.[18] The system also suggests that the court failed to find a willful violation.
We described in Taylor v. District Court for the Fourth Judicial District the inquiry a court must make concerning the element of willfulness in determining whether an indirect contempt has occurred.[19] There we said:
In order for there to be contempt it must appear that there has been a willful disregard or disobedience of the authority or orders of the court. Whether such willfulness exists is something the court cannot be aware of from its own observations in the courtroom and without inquiry from other sources. Without such inquiry the court cannot ascertain the operational facts from which an inference of willful disobedience or disregard of the court's authority or orders can be drawn.[[20]]
In this case, the system's alleged noncompliance with the court's orders was not observed by the superior court; rather, it was brought to the court's attention by class counsel's motion for an order to show cause.[21]
*881 In Taylor we stated that willfulness is the mens rea requirement for criminal contempt. "When a criminal contempt is involved, all elements of the offense, including that of willfulness, must be proven beyond a reasonable doubt."[22] "Willfulness is established by proof of conscious action and does not require a showing of specific intent."[23] We said in Continental Insurance Cos. v. Bayless & Roberts that "[i]f it is proved that a party had notice of the court's order and was aware of the requirements but failed to comply with the order, in the absence of explanation of the reason for such failure, a court could infer it to be intentional."[24] But we held in Bayless & Roberts that "[n]o findings of fact were made as to Continental's intent in disobeying the court's order."[25]
During the show cause hearing the superior court heard testimony from Charles Laird, the APFRS director and the administrator charged with implementing the court's orders. Laird explained how he, the APFRS lawyer, and the staff interpreted the orders, and discussed why he believed the system was in compliance. Laird explained the lengthy process of distributing the funds. He described sending out inquiries to the APFRS members to determine in which form each wished to receive payment, receiving the responses, and issuing the checks. He explained that this process could not be done in one day. He therefore did not interpret the April 6 order to mean that the letters transmitting the court's findings had to be sent on the first day any checks went out. The order referred to "the date enhancements are distributed to retirees." Laird testified that the process did not take place on just one day. Instead, he understood the order's reference to "the date enhancements are distributed to retirees" to refer to the span of time, as described in the CSA, in which the system was compelled to complete the processby late spring or early summer of 2000. He testified that he believed he was complying with the court's orders by sending the letters on June 8before the process was completedas opposed to sending the letters simultaneously with the payments. This was the only testimony the court heard regarding the system's alleged contempt. But there was other evidence before the court. This evidence included the April 6 order itself, the court file containing memoranda about how that order was to be interpreted and applied, the clarifying April 28 order, the text of the board's June 8 letter to the class members, and copies of May and June correspondence between counsel concerning what the system needed to do and when it needed to do it to comply with the April 6 order.
After receiving the Laird testimony, the court announced that it was holding the system in contempt. Counsel for the system asked the court to clarify its findings on the issue of willfulness. Earlier in the hearing, the court had articulated its understanding of the elements of contempt, stating, "There has to be a court order, and they have to have notice of the court order, and they have to have violated a court order, and they have to have been in a position to have not violated it." In response to counsel's inquiry about the issue of willfulness, the court stated:
I do not find that Mr. Laird is being dishonest.... But the fact is the board did something contrary to the specific terms of my order. Mr. Laird is not the one that's on the hot seat here today. It's the system that violated my order.... I find that the board, I don't know if it was Mr. Laird, I don't know if it was some particular member of the board, it might have been Mr. [Klausner], it might have been somebody from the Municipality, it might have been the man in the moon. I don't know who it was, but somebody influenced the *882 board and caused the board to make a decision in sending out the contradiction of my findings at the same time as the findings after they were supposed to have sent them out, with the particular intent of defying my order and interfering with the impact of my order, and they are in contempt for doing that.... They've acted like the thugs we put in the jury box every day handcuffed together, saying we don't respect the law, they don't respect the court. That's contempt. They ought to be ashamed of themselves. I'm very sorry they did this in the first place, and I'm really sorry that they didn't come in here today and say we got carried away by emotional stuff ... and we're sorry we got caught up in that. We don't mean the court any disrespect. But they didn't come in here and say that, so they're in contempt.[[26]]
(Emphasis added.)
The system's attorney then argued that the system, acting through Laird, "did not intentionally defy the court's order." The court responded, "I find to the contrary...." The court later observed, in discussing Klausner's role, that "his client's purpose as I mentioned before seems culpable in that it seems tied in with an intent to interfere with and negate the rulings [of] the court."
Thus, the court first found that the system had decided to send out the letter contradicting the court's findings, "after they were supposed to have sent them out, with the particular intent of defying my order and interfering with the impact of my order...." Second, by announcing that "I find to the contrary," the court expressly rejected the system's assertion that the system did not intentionally defy the order. These findings satisfy the requirement of a willful violation. We therefore reject the system's argument that the court misdefined the elements of contempt and failed to find a willful violation.
It does not matter that the court, when it first discussed the contempt sanction, did not specifically mention the willfulness element. After the system's attorney asked the court about that element at the hearing, the court made the findings quoted above.
It also does not matter that the court did not specify who caused the board to defy the order. It was the system which the court held in contempt. It also does not matter that the court stated that it did not find that Laird was being dishonest, because the court found that "somebody influenced the board" and caused it to act "with the particular intent of defying my order...."
C. The Finding of Willfulness Was Not Clearly Erroneous.
We also conclude that there was sufficient evidence to support the finding of willfulness. This included Laird's testimony that he had written the first draft of the board's letter, but that it was "reviewed by a number of people before it was finalized." This testimony permits an inference that the reason the information was mailed untimely was delay in drafting and revising the letter the board wanted to send with the intention of contradicting and "undermining" the court's reasons for the award and the court's comments responding to criticism of class counsel. Further, the court's stated purpose for ordering the informational mail-out requires an inference that, notwithstanding Laird's personal innocence, the system collectively recognized the importance of simultaneously sending the court's comments when it made any payments to members of the class. This evidence also permits an inference that the system willfully violated the order by beginning to make payments to the class members some three weeks before it sent the court's explanatory comments.
We also reject the system's assertions that the April 6 order was ambiguous. The order specified that the court's comments were to be sent to "each of the APFRS members ... no later than the date enhancements are distributed to retirees." This language made it clear that payment could not be made to a *883 member before the information was sent to that member. Further, as appellees argue on appeal, there is no indication the system's attorney, Klausner, thought the information-distribution requirement was ambiguous. The letters class counsel and Klausner exchanged in May and early June 2000 strongly imply that Klausner understood that the information was to have been mailed when the payments began. As the days passed and class counsel became more strident and even threatened a contempt request, Klausner never asserted that the mail-out requirement was ambiguous or that the system had months in which to comply. These exchanges also tend to confirm the superior court's suspicion that the system intentionally delayed sending the court's comments to the members until the board could prepare and send its letter "contradicting" the court's attorney's fees findings.
The system also argues that because it was impossible to make all of the payments simultaneously, it also would have been impossible to comply with the April 6 order if it had been written as the court interpreted it. But the impossibility of paying each member on the same day did not prevent the system from distributing the information to each member at the same time it paid that member, or from sending the information to each member before it made the first payment to any member.

D. Standard of Proof
The system contends that the court failed to apply the reasonable doubt standard of proof. The reasonable doubt standard of proof applies to criminal contempt proceedings.[27] The superior court did not specify the standard of proof it was applying to the contempt proceeding. We have held in other contexts that a trial court need not explicitly state all of its factual findings so long as its findings are "adequate to reveal its reasoning process."[28] Courts elsewhere have held that a trial court need not explicitly state the standard of proof it is applying if there is no dispute about the applicable standard.[29] We will normally assume that the trial court has applied the correct standard.
The court's August 22 clarification order, which explained the changes to which Klausner was to respond at the August 23 hearing, cited AS 09.50.010(5). That statute defines contempt to include "disobedience of a lawful judgment, order, or process of the court." Thus, the court was aware that a violation of AS 09.50.010(5) encompassed violations of court orders. The court was of course aware that it had required the system to show cause why it should not be sanctioned for violating a court order. Reported Alaska case law establishes that subsection .010(5) deals with criminal, rather than civil, contempt, at least if the court's purpose is to punish rather than coerce.[30] The sanction here had no possible coercive effect. It is undisputed that the elements of criminal contempt are subject to a beyond a reasonable doubt standard of proof in Alaska. Decisions so holding are cited and described in the annotations to AS 09.50.010.[31] From this we *884 can safely assume the superior court recognized and applied the correct standard.
There is no indication the court applied some other standard. The court did not mention the lesser preponderance or clear and convincing standards. The contempt hearing commenced with an oral argument by Klausner's counsel that emphasized the punitive nature of the proceedings against Klausner. Referring to the size of the maximum potential fine, counsel also requested a jury trial and analogized to Baker v. City of Fairbanks,[32] which counsel described as stating that a large enough fine connotes criminal conduct.
Given the context of these arguments, and absent any reason to think otherwise, we assume the court applied the correct standard of proof.

IV. CONCLUSION
For these reasons, we AFFIRM the order holding the system in contempt.
FABE, Chief Justice, not participating.
NOTES
[1]  Former Anchorage Municipal Code (AMC) 03.85.030-.040.
[2]  AMC 03.85.030(B), (C).
[3]  Gallion v. Municipality of Anchorage (Gallion I), 944 P.2d 436, 438-39 (Alaska 1997), describes these circumstances in detail.
[4]  Id. at 439.
[5]  Id. at 439-40.
[6]  Id. at 443.
[7]  The class members moved for summary judgment in 1999. The superior court held that the board owed a fiduciary duty only to the members. It ruled that the members had no right to increased benefits, but it directed the board to recommend a proposal to the municipal assembly addressing the surplus. The municipality intervened and cross-moved for summary judgment seeking to establish a reversionary interest in the surplus. The court denied the municipality's motion, finding no such interest existed. Despite this order, the CSA granted the municipality $40 million from the surplus.
[8]  The system claimed that distributing the funds was a gradual process that required the system to liquidate investments to produce cash for distribution, educate the members about the payments, and wait for each recipient to determine in what form he or she wanted to receive payment before distribution of the funds could begin.
[9]  The board's letter stated that it contained "court-related materials from the hearing" on attorney's fees and stated that they were sent because class counsel had asked the superior court to order that they be sent. The letter then stated that the board considered that sending the materials was a "waste of trust assets." The letter also told members that the board "believed that the award of additional [class counsel attorney's] fees, to be deducted from [members'] benefit payments, was wrong."
[10]  The parties do not distinguish between the system and the board for purposes of the issues on appeal.
[11]  Guin v. Ha, 591 P.2d 1281, 1284 n. 6 (Alaska 1979) (holding that on questions of law we adopt rule "that is most persuasive in light of precedent, reason, and policy").
[12]  E.g., A.B. v. State, Dep't of Health & Soc. Servs., 7 P.3d 946, 950 (Alaska 2000) (citation omitted) ("Whether the trial court's findings comport with the child in need of aid statutes is a question of law that this court reviews de novo.").
[13]  Alaska Rule of Civil Procedure 90(b) reads:

For every contempt other than [contempts committed in the presence of the court], upon a proper showing on ex parte motion supported by affidavits, the court shall either order the accused party to show cause at some reasonable time, to be therein specified, why he should not be punished for the alleged contempt, or shall issue a bench warrant for the arrest of such party. Such proceeding may be commenced and prosecuted in the same action or in an independent proceeding either by the state, or by the aggrieved party whose right or remedy in an action has been defeated or prejudiced or who has suffered a loss or injury by the act constituting a contempt.
[14]  Matanuska Elec. Ass'n, Inc. v. Rewire the Board, 36 P.3d 685, 700-01 (Alaska 2001) (noting clear error standard when reviewing contempt orders is "consistent with the deferential review used by courts in other jurisdictions" and citing cases illustrating deferential standards of other states).
[15]  The system's briefs focus on the April 6 order. In its oral contempt order the superior court explicitly mentioned only the April 6 order but also seemed to take the April 28 order into consideration.
[16]  Johansen v. State, 491 P.2d 759, 763 (Alaska 1971) (citing Gompers v. Buck's Stove & Range Co., 221 U.S. 418, 441, 31 S.Ct. 492, 55 L.Ed. 797 (1911)).
[17]  See Hutchison v. State, 27 P.3d 774, 779 (Alaska App.2001).
[18]  In L.A.M. v. State, 547 P.2d 827, 831 (Alaska 1976), we explained that the four elements of contempt are:

(1) the existence of a valid order directing the alleged contemnor to do or refrain from doing something and the court's jurisdiction to enter that order; (2) the contemnor's notice of the order within sufficient time to comply with it;... (3) the contemnor's ability to comply with the order; and (4) the contemnor's willful failure to comply with the order.
[19]  434 P.2d 679, 681 (Alaska 1967).
[20]  Taylor, 434 P.2d at 681 (citations omitted).
[21]  The system argues that class counsel's motion was insufficient because it was not supported by affidavits. We have ruled that the purpose of Civil Rule 90(b)'s affidavit requirement is to ensure procedural due process for the person charged. Taylor, 434 P.2d at 681-82. In Taylor we held that the order to show cause specifying the contemptuous act satisfied the notice requirement of procedural due process. In this case, the motion for an order to show cause specified the allegedly contemptuous acts and delineated what actions the system would have to defend. An affidavit would have been redundant. See id.
[22]  Continental Ins. Cos. v. Bayless & Roberts, Inc., 548 P.2d 398, 407 (Alaska 1976) (citations omitted).
[23]  Rollins v. State ex rel. Municipality of Anchorage, 748 P.2d 767, 771 (Alaska App.1988) (citing Hentzner v. State, 613 P.2d 821, 826 (Alaska 1980)).
[24]  Bayless & Roberts, 548 P.2d at 407 (citations omitted).
[25]  Id. at 400.
[26]  "[T]he contradiction of my findings" is a reference to the letter the board wrote and sent out to the members with the copy of the court's attorney's fees award. The letter the board wrote expressed, among other things, the board's disagreement with the court's April 6 order and attorney's fees award.
[27]  Continental Ins. Cos. v. Bayless & Roberts, Inc., 548 P.2d 398, 407 (Alaska 1976); Carter v. Brodrick, 750 P.2d 843, 845 (Alaska App.1988).
[28]  Borchgrevink v. Borchgrevink, 941 P.2d 132, 137 (Alaska 1997) (holding in child custody context that court not required to make "wrap-up" finding); see also Virgin v. Virgin, 990 P.2d 1040, 1047-48 (Alaska 1999) (noting that requiring "wrap-up" finding "would unjustifiably elevate form over substance").
[29]  Ross v. Superior Court, 19 Cal.3d 899, 141 Cal.Rptr. 133, 569 P.2d 727, 737 (1977) ("[T]he applicability of the reasonable doubt standard to contempt proceedings has ... been firmly established in a long line of California decisions, and thus in the instant case there is no reason to depart from the normal presumption that the trial court properly followed established law."); Johnson v. De Toledo, 61 Conn.App. 156, 763 A.2d 28, 32 (2000); In re C.T., 724 A.2d 590, 597 (D.C.1999); State v. Kotis, 91 Hawai'i 319, 984 P.2d 78, 99 (1999); State v. Hazelton, 267 Kan. 384, 985 P.2d 698, 701 (1999); Ex parte Jackson, 911 S.W.2d 230, 234 (Tex.App.1995) ("While relator is apparently correct that a `beyond a reasonable doubt' standard should be applied, there is no evidence that a lesser standard was applied. The trial court, sitting without a jury is presumed to have used the correct standard of proof absent a showing to the contrary.").
[30]  L.A.M. v. State, 547 P.2d 827, 832 (Alaska 1976).
[31]  See, e.g., Continental Ins. Cos. v. Bayless & Roberts, Inc., 548 P.2d 398 (Alaska 1976).
[32]  471 P.2d 386 (Alaska 1970).
