WIGGINS, Circuit Judge:
OVERVIEW
In 1985, approximately 2,400 residents of the City of Tucson (“the Valenzuela claims”) sued Hughes Aircraft Company (“Hughes”) for injuries arising out of contamination of their drinking water due to Hughes’ practice of discharging trichloroethylene (“TCE”) into unlined ponds. In 1991, Hughes settled the Valenzuela claims with a payment of almost $85 million. Ronald John Smith and other Lloyd’s underwriters (“Lloyd’s”), Hartford Accident and Indemnity Company (“Hart[1451]*1451ford”), and Insurance Company of North America (“INA”) (collectively referred to as “Insurers”) brought declaratory judgment actions beginning in 1988 to determine them respective liability for the Valenzuela claims.
On September 6, 1991, the district court granted summary judgment for the Insurers with respect to policies issued between 1971 and 1985, 783 F.Supp. 1222. On March 19, 1992, the district court declined to review a $55,777.83 award for Hartford’s deposition costs that was issued by the district court clerk. Finally, on September 16, 1992, the district court granted summary judgment for INA and Lloyd’s with respect to policies issued between 1956 and 1971. Hughes timely appealed each decision. We have jurisdiction pursuant to 28 U.S.C. § 1291. We affirm in part and reverse in part.
I. Standard of Review
We review de novo the district court’s grants of summary judgment. See FDIC v. O’Melveny & Meyers, 969 F.2d 744, 747 (9th Cir.1992), cert. filed, 62 U.S.L.W. 3275 (Sept. 27, 1993); Musick v. Burke, 913 F.2d 1390, 1394 (9th Cir.1990). Viewing the evidence in the light most favorable to Hughes, we must determine “whether there are any genuine issues of material fact for trial, and whether the district court correctly applied the relevant substantive law.” See O’Melveny & Meyers, 969 F.2d at 747. We also review de novo the district court’s interpretation of state law. Salve Regina College v. Russell, 499 U.S. 225, 231, 111 S.Ct. 1217, 1221, 113 L.Ed.2d 190 (1991); Brooks v. Hilton Casinos, Inc., 959 F.2d 757, 759 (9th Cir.), cert. denied, — U.S. -, 113 S.Ct. 300, 121 L.Ed.2d 224 (1992).
II. Merits
A. The September 6, 1991, Order Granting Summary Judgment for Insurers. (Nos. 91-16758, 91-16876, & 91-16877)
1. The AVN I6A Pollution Exclusion.
The district court concluded that the language of AVN 46A unambiguously excluded pollution risks not only in the aviation policies, but also in the excess CGL policies.1 Hughes argues that the drafting history of AVN 46A and the testimony of key Lloyd’s witnesses demonstrate that Lloyd’s never intended the exclusion to apply to anything but aviation coverage. The district court refused to consider this evidence because Hughes “failed to tie it to the parties’ intent.” We agree with Hughes. Hughes presented evidence from Hughes’ former insurance manager that his understanding of AVN 46A was based in part on AVN 46A’s drafting history. Because it is unclear from the language of the exclusion whether AVN 46A applied to the CGL policy, this evidence is admissible to indicate the real agreement of the parties. See Darner Motor Sales v. Universal Underwriters Ins. Co., 140 Ariz. 383, 393, 682 P.2d 388, 398 (1984); Pacific Gas & Elec. Co. v. G.W. Thomas Drayage & Rigging Co., 69 Cal.2d 33, 69 Cal.Rptr. 561, 564, 442 P.2d 641, 644 (1968) (allowing extrinsic evidence to determine the parties’ intent).2
Hughes also presented evidence that its agents understood AVN 46A to apply only to aviation risks. Moreover, the plain language of AVN 46A, when read in its entirety, contains ambiguities that preclude summary judgment. For example, the AVN abbreviation denotes that the exclusion came from the aviation form book; the first AVN 46A exclusion, for noise, vibration, and sonic booms, [1452]*1452appears to apply only to airplanes; and all four AVN 46A exclusions are subject to an exception for “a crash, explosion or collision or a recorded in-flight emergency causing abnormal aircraft operation.” Thus, because Hughes’ interpretation of the evidence regarding its understanding of AVN 46A supports the conclusion that the exclusion did not apply to non-aviation risks, we reverse the grant of summary judgment.
2. The “Sudden and Accidental” Exception to the Pollution Exclusion.
The district court concluded, as a matter of law, that the so-called pollution exclusion contained in the Insurers’ 1974-1985 policies precluded coverage. The pollution exclusion contains an exception for “sudden and accidental” discharges.3 The district court concluded that this exception did not apply because (1) under both Arizona and California law, the definition of “sudden” incorporates a notion of temporal brevity and does not merely mean unexpected; and (2) under the Valenzuela facts, the claimants’ injuries were the result of pollution that was not “sudden.” We agree.
a. “Sudden” Connotes Temporal Brevity.
Under Arizona law, the district court correctly concluded that the phrase “sudden and accidental” is ambiguous because different jurisdictions have interpreted the provision differently. See Federal Ins. Co. v. P.A.T. Homes, Inc., 113 Ariz. 136, 138-39, 547 P.2d 1050, 1052-53 (1976), disapproved on other grounds, State Farm Mut. Auto. Ins. Co. v. Wilson, 162 Ariz. 251, 258, 782 P.2d 727, 734 (1989); see also Intel Corp. v. Hartford Acc. & Indem. Co., 952 F.2d 1551, 1561 (9th Cir.1991) (recognizing disparate interpretations of the “sudden and accidental” exception). This ambiguity is properly analyzed under State Farm Mut. Auto. Ins. Co. v. Wilson, 162 Ariz. 251, 257-58, 782 P.2d 727, 733-34 (1989). The district court properly (1) looked to the language of the exclusion and concluded that “sudden” “unmistakably connotes a temporal quality” (otherwise, it would simply be a synonym for “accidental”); (2) concluded that requiring temporal brevity furthered public policy by excluding deliberate indifference on the part of a polluting insured; and (3) analyzed the purpose of the transaction and, noting that Hughes is not an unsophisticated consumer, concluded that “an interpretation of ‘sudden’ that fails to recognize its temporal quality” would frustrate the parties’ intent by forcing the Insurers to buy into the risk of insuring a pollution prone operation. See id. We agree with and adopt the district court’s analysis and conclude that, under Arizona law, the “sudden and accidental” exception “unmistakably connotes a temporal quality.”
Under California law, the district court summarily concluded that no ambiguity existed, citing only United States Fid. & Guar. Co. v. Morrison Grain Co., 734 F.Supp. 437, 446-47 (D.Kan.1990), aff'd, 999 F.2d 489 (10th Cir.1993). However, the district court’s cursory conclusion is consistent with California law. The “clear and explicit” meanings of insurance contract provisions, interpreted in their “ordinary and popular sense,” control judicial interpretation. AIU Ins. Co. v. Superior Court, 51 Cal.3d 807, 274 Cal.Rptr. 820, 831, 799 P.2d 1253, 1264 (1990). Using this standard, California courts have concluded that the phrase “sudden and accidental” is not ambiguous. Shell Oil Co. v. Winterthur Swiss Ins. Co., 12 Cal.App.4th 715, 15 Cal.Rptr.2d 815, 841 (1993); Truck Ins. Exch. v. Pozzuoli, 17 Cal.App.4th 856, 21 Cal.Rptr.2d 650, 651 (Ct.App.1993); ACL Technologies, Inc. v. Northbrook Prop. & Cas. Ins. Co., 17 Cal.App.4th 1773, 22 Cal.Rptr.2d 206, 213-14 (1993). Moreover, California courts have indicated that “sudden” connotes a temporal quality.
[1453]*1453[Accidental conveys the sense of an unexpected or unintended event, while “sudden” conveys the sense of an unexpected event that is abrupt or immediate in nature. “Sudden and accidental” is not ambiguous if we give the words their full significance. A court should not make a phrase ambiguous by unreasonably truncating a word’s meaning.
Shell Oil, 15 Cal.Rptr.2d at 841; ACL Technologies, 22 Cal.Rptr.2d at 214. Therefore, under California law, non-sudden, continuous pollution does not qualify as an exception to the pollution exclusion in this case. See Shell Oil, 15 Cal.Rptr.2d at 841-42; Pozzuoli, 21 Cal.Rptr.2d at 651-52.
Hughes argues that the pollution exclusion was drafted as a mere “clarification” of the “occurrence” definition contained in prior CGL policies and that the insurance industry, in selling the new exclusion, stated that the new pollution exclusion did not reduce coverage. However, we agree with the district court that the drafting and marketing history of the pollution exclusion is not only unclear but also irrelevant because Hughes has not shown that it relied on this history or that the history played any part in the policy negotiations. See AIU, 274 Cal.Rptr. at 832 n. 9, 799 P.2d at 1265 n. 9; Darner Motor, 140 Ariz. at 393, 682 P.2d at 398 (explaining that extrinsic evidence must show the parties’ intent with regal’d to the negotiation of the agreement). Accordingly, we conclude that under Arizona and California law, the “sudden and accidental” exception to the pollution exclusion necessarily incorporates a notion of temporal brevity.
b. The Valenzuela Claims were Caused by Hughes’ Gradual, Non-Sudden Pollution.
Hughes further argues on two grounds that the pollution exclusion does not exclude coverage: (1) TCE was not a contaminant or pollutant within the pollution exclusion for most of the relevant time period and (2) certain “sudden” polluting events contributed to the Valenzuela injuries. We disagree.
First, the fact that TCE was not listed as a pollutant by the EPA until the late 1970’s does not help Hughes because the language of the exclusion does not require such a listing. The pollution exclusion excludes injuries arising out of the “discharge, dispersal, [or] release” of, inter alia, “toxic chemicals, liquids or gases, [or] waste materials or other irritants.” Because Hughes does not and could not claim that TCE is not a toxic chemical, liquid, waste material, or irritant, we reject its first ground. Moreover, because Hughes raises this argument for the first time on appeal, Hughes has waived it. See Gruver v. Midas Intern. Corp., 925 F.2d 280, 283 (9th Cir.1991).
Second, Hughes’ argument that certain “sudden” polluting events partially caused the injuries to the Venezuela claimants also fails. These “sudden” polluting events caused TCE and other toxic chemicals to be dumped directly into Hughes’ unlined ponds. They occurred when the waste treatment plant broke down or was over-capacitated or when TCE was spilled onto the work floor and was pushed into a drain that bypassed the treatment plant. The district court properly rejected Hughes’ effort to “break down its long-term waste practices into temporal components in order to find coverage where the evidence unequivocally demonstrates that the pollution was gradual.” Accordingly, we affirm the district court’s grant of summary judgment for the Insurers regarding the pollution exclusion.
B. The March 19, 1992, Order Declining to Revieiv the Clerk’s Award of Costs to Hartford. (No. 92-15815)
Based on its summary judgment victory in the September 6, 1991, order, Hartford filed an application for costs. Hartford sought costs of $62,170.73, the vast majority of which were reimbursemént for Hartford’s 20% share of deposition costs under a cost-sharing agreement with the other insurers. After a hearing, the district court clerk granted Hartford $55,777.83. Hughes filed a motion for review pursuant to Fed.R.Civ.P. 54(d). The district court (1) denied Hughes’ motion as untimely and (2) concluded that had Hughes’ motion been timely, it would have denied the motion on the merits because the depositions for which Hartford sought reim[1454]*1454bursement were “necessarily obtained.” We agree with the district court’s second conclusion.4
We review the district court’s determination of the nature and amount of the costs award for an abuse of discretion. Haagen-Dazs Co. v. Double Rainbow Gourmet Ice Creams, Inc., 920 F.2d 587, 588 (9th Cir.1990). Hughes argues that the district court erred (1) by creating a presumption that Hartford’s deposition costs were “necessarily obtained” and (2) by concluding that the costs were “necessarily obtained” even though Hartford failed to detail why each of the depositions was necessary. We disagree.
First, as the district court correctly noted, this court has not clearly allocated between the prevailing and losing party the burden of demonstrating whether deposition costs are “necessarily obtained” under 28 U.S.C. § 1920. The district court relied on out-of-circuit cases that appear to place the burden on the losing party. See Hudson v. Nabisco Brands, Inc., 758 F.2d 1237, 1242 (7th Cir.1985), overruled on other grounds, Provident Bank v. Manor Steel Corp., 882 F.2d 258, 261 (7th Cir.1989); Desisto College v. Town of Howey-In-The-Hills, 718 F.Supp. 906, 910 (M.D.Fla.1989), aff'd, 914 F.2d 267 (11th Cir.1990) (table). However, we need not address this question because the district court independently determined that Hartford’s deposition costs were necessary.
Second, we reject Hughes’ contention that the district court could not conclude that the deposition costs were “necessarily obtained” because Hartford failed to detail why each deposition was necessary. The district court’s order specifically addresses each category of depositions and adequately explains why they were necessary for Hartford. In light of the fact that the district court was “intimately familiar” with the proceedings that led to the imposition of costs, we conclude that the district court did not abuse its discretion by concluding that Hartford’s deposition costs were “necessarily obtained.” See Haagen-Dazs, 920 F.2d at 588.
C. The September 16, 1992, Order Granting Summary Judgment for INA and Lloyd’s. (Nos. 92-16901 & 92-16957)
1. The “Expected” or “Intended” Requirement.
a. The District Court Properly Inferred an Exclusion for “Expected” or “Intended” Damage.
The district court inferred an exclusion into the pre-1971 policies for damages that Hughes “expected or intended.” The court further ruled that a subjective standard should be used to measure Hughes’ intent. Hughes contends that this inference was error. Specifically, Hughes argues that the district court erred by extending the public policy stated in California Insurance Code § 533 to include “expected” harm.5 We disagree.
“A ‘willful act’ under section 533 must ... include a deliberate liability-producing act that the individual, before acting, expected to cause harm.” Shell Oil, 15 Cal.Rptr.2d at 833. “[S]eetion 533 precludes indemnification for liability arising from deliberate conduct that the insured expected or intended to cause damage.” Id. Accordingly, INA and Lloyd’s are not liable for any bodily injury caused by Hughes’ conduct that Hughes subjectively expected or intended to cause. See id. at 833-35.
Hughes also contends that the district court erred in failing to admit extrinsic evidence that INA believed that policies similar to the policies in this case provided coverage for “expected” harm. However, these memoranda and letters were not created before 1970, after Hughes’ INA policies had expired, and were therefore never seen, much less relied upon by Hughes during its [1455]*1455negotiations with INA. Therefore, we conclude that Hughes’ extrinsic evidence is neither persuasive nor relevant and that the district court properly refused to consider it. See AIU, 274 Cal.Rptr. at 832-33, 799 P.2d at 1265-66.
b. The District Court Erred in Ruling that Hughes Expected or Intended the Injuries.
In granting summary judgment, the district court concluded that Hughes “expected” the damage that it caused the Valenzuela claimants. “The appropriate test for ‘expected’ damage is whether the insured knew or believed its conduct was substantially certain or highly likely to result in that kind of damage.” Shell Oil, 15 Cal.Rptr.2d at 836. We conclude that summary judgment was inappropriate because it is not clear whether Hughes’ conduct meets this test.
First, the district court improperly based its conclusion that Hughes expected or intended the Valenzuela injuries, in large part, on Hughes’ disposal of chromium. This was error because the Valenzuela injuries were not caused by chromium contamination. There is no evidence that the Valenzuela claimants were ever exposed to harmful levels of chromium; the Valenzuela wells never contained excess chromium and were never closed based on chromium contamination. Rather, the City of Tucson closed wells because of the presence of organic solvents like TCE. Accordingly, on remand the district court should not rely on evidence of Hughes’ chromium disposal practices.
Second, the evidence that Hughes expected or intended injuries caused by TCE contamination is insufficient for summary judgment. In reaching its conclusion that Hughes expected or intended to cause injuries by its disposal of TCE, the district court relied on evidence that TCE was toxic in some concentration if ingested. However, Hughes raises a genuine issue of material fact by arguing that, until recently, exposure to moderate amounts of TCE was not considered harmful. TCE was commonly used as an anesthetic and disinfectant. It was also used to extract hops, decaffeinate coffee, and to prepare fish meal. It was not until 1977 that the FDA first proposed banning TCE as a food additive. The first recommended, non-binding TCE standard for drinking water was not promulgated by the EPA until 1979. Moreover, Hughes introduced evidence that the common and preferred method of disposing of TCE was to put it on the ground to evaporate. Further, throughout the applicable period, regulatory agencies did not comment on Hughes’ TCE disposal practices.
In light of this evidence, we cannot conclude that Hughes “knew or believed its [disposal of TCE] was substantially certain or highly likely to result” in harm to the Valenzuela claimants. See Shell Oil, 15 Cal.Rptr.2d at 836. Accordingly, we reverse this ground for the district court’s grant of summary judgment.
2. The Requirement that Injuries Must Occur During the Policy Period.
a. The District Court Properly Inferred a Requirement that the Valenzuela Injuries Must Occur During the Policy Period.
INA’s CGL policies (and Lloyd’s excess policies) provide Hughes insurance coverage for “occurrences which occur during the policy period anywhere.” However, with respect to bodily injury coverage, the word “occurrence” is not defined. The district court concluded that an “occurrence” could happen only if the Valenzuela claimants were injured during the policy period. Therefore, Hughes’ act of dumping TCE was not an “occurrence” by itself; someone had to be injured first. We agree.
The general rule in California is that [t]he insurer’s obligation to pay is ordinarily triggered when the insured is liable to a third party for injuries or damages caused by an “occurrence” or “accident,” and the time of the “occurrence” is “not the time the wrongful act was committed, but the time the complaining party was actually damaged.”
Chu v. Canadian Indem. Co., 224 Cal.App.3d 86, 274 Cal.Rptr. 20, 25-26 (1990) (quoting Remmer v. Glens Falls Indem. Co., 140 Cal.[1456]*1456App.2d 84, 295 P.2d 19, 21 (1956)); see also Hallmark Ins. Co. v. Superior Court, 201 Cal.App.3d 1014, 247 Cal.Rptr. 638, 640 (1988); State Farm Mut. Auto. Ins. Co. v. Longden, 197 Cal.App.3d 226, 242 Cal.Rptr. 726, 729-30 (1987). Hughes contends that the general rule does not apply in this case, citing only Insurance Co. of N. America v. Sam Harris Constr. Co., 22 Cal.3d 409, 149 Cal.Rptr. 292, 583 P.2d 1335 (1978). We disagree.
In Sam Hams, the court found coverage even though the complaining party was injured outside the policy period. The court departed from the general rule because it found that the policy phrase “occurrences or accidents” was ambiguous where neither “occurrence” nor “accident” was defined in the policy. Id. 149 Cal.Rptr. at 293, 583 P.2d at 1336. However, Sam Harris is distinguishable from this case because Sam Hams places great emphasis on the undefined disjunctive phrase “occurrences or accidents,” whereas in this case only the phrase “occurrence” is used. See Longden, 242 Cal.Rptr. at 730 (distinguishing Sam Harris because the policy in Longden did not contain the disjunctive phrase “occurrence or accidents” but referred only to “accidents”); Employer Cas. Co. v. Northwestern Nat’l Ins. Group, 109 Cal.App.3d 462, 167 Cal.Rptr. 296, 299-300 (1980) (same), overruled on other grounds, In re Marriage of Arceneaux, 51 Cal.3d 1130, 275 Cal.Rptr. 797, 801, 800 P.2d 1227, 1231 (1990). Accordingly, the general rule applies, and INA and Lloyd’s are not liable for any injuries that occurred after the relevant policy period ended. See Chu, 274 Cal.Rptr. at 25-26.
b. The District Court Erred in Ruling that the Valenzuela Injuries Occurred after the Pre-1971 Policies Expired.
In concluding that no Valenzuela claimant was injured during the relevant policy periods, the district court relied on expert evidence that Hughes had developed to defend itself in the underlying Valenzuela tort action. These experts plotted the underground TCE contamination from Hughes’ ponds to Tucson drinking water wells. They concluded that contaminants moved too slowly to affect all but one of the wells before the policies terminated in 1971. They further concluded that no harm was caused by the contaminated well because that water was mixed with uncontaminated water and was thus rendered harmless during the policy period.
However, Hughes offered expert evidence that was developed by the Valenzuela claimants. These experts concluded that Tucson’s municipal wells were contaminated with TCE from Hughes’ property beginning no later than 1956. They also concluded that any level of TCE is harmful and causes bodily injury. The district court refused to hear this testimony because Hughes had failed to “designate” these experts before a discovery deadline. The district court also found that the evidence, even if it were timely presented, was not as credible as the experts Hughes had previously retained.
We review for an abuse of discretion the district court’s discovery rulings. United States v. Bourgeois, 964 F.2d 935, 937 (9th Cir.), cert. denied, — U.S. -, 113 S.Ct. 290, 121 L.Ed.2d 215 (1992). The district court’s requirement that the expert testimony be designated refers to a discovery order requiring the parties to designate their retained expert witnesses. However, in this ease, none of the Valenzuela experts were ever “retained” by Hughes. Because the Valenzuela expert evidence clearly supports a finding that some of the Valenzuela injuries occurred prior to 1971, we conclude that the district court abused its discretion in failing to review it. Moreover, the district court’s conclusion that the Valenzuela experts were less credible is inappropriate at summary judgment. See Musick, 913 F.2d at 1394. Accordingly, because a genuine issue of material fact exists regarding whether some Valenzuela claimants were injured pri- or to 1971, we reverse the district court’s grant of summary judgment.
AFFIRMED in part; REVERSED in part; and REMANDED. Each party shall bear its own costs on appeal.