Which methods require the separation of elements of accrued depreciation into various categories?

The observed condition method and the engineering breakdown method specifically require the separation of elements of accrued depreciation into various categories. This is because both methods analyze the property in detail to identify different causes of depreciation, allowing for a more precise quantification of each component's impact on value.

In the observed condition method, appraisers assess the physical state of a property and categorize depreciation into physical deterioration, functional obsolescence, and economic obsolescence. This detailed examination helps identify exactly where value is lost, enabling more accurate adjustments during the appraisal process.

Similarly, the engineering breakdown method involves a detailed evaluation of the property's components, where each element is analyzed for its replacement cost and the amount of depreciation that has occurred. By breaking down the elements, appraisers can better assess how much each part of the property contributes to overall depreciation, considering age, wear and tear, and market factors.

Other methods, such as those in the income or cost approaches, may consider depreciation but do not require the same level of detailed breakdown into categories. Therefore, the correct choice focuses specifically on the methods that necessitate this comprehensive separation for an accurate appraisal process.