Goodwill is evaluated for impairment on at least an annual basis, or more frequently if indicators of impairment exist. The annual impairment tests are based on Level 3 inputs (see Note 13—Fair Value Measurement). During the first quarter of 2020, the Company had triggering events related to the significant adverse change to the demand for the Company’s services in connection with a significant decline in the price of oil and the related global economic impacts resulting from the OPEC+ disputes as well as the COVID-19 pandemic. This included uncertainty regarding oil prices and the length of the recovery following the significant market disruption in the oil and gas industry. Given the volatile market environment at March 31, 2020, the Company utilized third-party valuation advisors to assist with these evaluations. These evaluations included significant judgment, including management’s short-term and long-term forecast of operating performance, discount rates based on our weighted-average cost of capital, revenue growth rates, profitability margins, capital expenditures, the timing of future cash flows based on an eventual recovery of the oil and gas industry, and in the case of long-lived assets, the remaining useful life and service potential of the asset. The Company performed quantitative tests for reporting units in both the Water Services and Water Infrastructure segments using the income and market approaches, resulting in a full impairment to goodwill in both segments.

During 2019, the Affirm goodwill was reduced to zero from the crane divestiture and impairment. The $4.4 million of goodwill impairment was based on the expected proceeds from selling and winding down the rest of the Affirm business following the Affirm crane business divestiture. Also, in connection with the Company’s segment realignment, the Company reallocated goodwill from one reporting unit in the 2018 Water Solutions segment to reporting units in the 2019 Water Services and Water Infrastructure segments using the reporting units’ relative fair values as of March 31, 2019.

The changes in the carrying amounts of goodwill by reportable segment for the years ended December 31, 2020, and 2019 are as follows:

(1)

See Note 3―Acquisitions and Divestitures for additional information.

The components of other intangible assets as of December 31, 2020 and 2019 are as follows:


	As of December 31, 2020								As of December 31, 2019
	Gross				Accumulated		Net		Gross		Accumulated		Net
	Value		Impairment		Amortization		Value		Value		Amortization		Value

	(in thousands)								(in thousands)
Definite-lived
Customer relationships	$	116,554	$	—	$	(29,302)	$	87,252	$	116,554	$	(20,233)	$	96,321
Patents		9,741		—		(3,166)		6,575		10,110		(2,420)		7,690
Other		7,234		—		(6,373)		861		7,234		(4,766)		2,468
Total definite-lived		133,529		—		(38,841)		94,688		133,898		(27,419)		106,479
Indefinite-lived
Water rights		7,031		—		—		7,031		7,031		—		7,031
Trademarks		23,442		(9,082)		—		14,360		23,442		—		23,442
Total indefinite-lived		30,473		(9,082)		—		21,391		30,473		—		30,473

Total other intangible assets, net	$	164,002	$	(9,082)	$	(38,841)	$	116,079	$	164,371	$	(27,419)	$	136,952

Due to the triggering events discussed above, the Company also tested all intangible assets for impairment during the first quarter of 2020. These evaluations included significant judgment, including discount rates based on our weighted-average cost of capital and the royalty rate. This resulted in $9.1 million of impairment to trademarks using the relief from royalty method, which was recorded in the Oilfield Chemicals segment.

During the year ended December 31, 2020, the Company added no new intangible assets. During the year ended December 31, 2019, the Company added $0.5 million in customer relationships. The weighted-average amortization period for customer relationships, patents and other definite-lived intangible assets as of December 31, 2020 was 9.7 years, 6.8 years and 2.7 years, respectively.

The indefinite-lived water rights and trademarks are generally subject to renewal every five to ten years.

Amortization expense of $11.7 million, $11.9 million and $13.1 million was recorded for the years ended December 31, 2020, 2019 and 2018, respectively. Annual amortization of intangible assets for the next five years and beyond is as follows:


Year Ending December 31,	Amount
	(in thousands)
2021	$	10,466
2022		10,252
2023		10,180
2024		10,111
2025		9,948
Thereafter		43,731
Total	$	94,688