(a) "Actual assessed value" means the assessed value of real property prior to the calculation of any transitional assessed value, and which is not reduced by any exemption from real property taxes.

(b) "Aggregate physical increase" means the sum of physical increases for assessment rolls completed from two thousand fourteen through two thousand twenty.

(c) "Annual tax" means the amount of real property tax that is imposed on a property for a fiscal year, determined after reduction for any amount from which the property is exempt, or which is abated, pursuant to applicable law.

(d) "Annual tax attributable to improvements" means the annual tax, multiplied by a fraction, the numerator of which is equal to the assessed value attributable to improvements on the property for the fiscal year, and the denominator of which is the total assessed value of the property for such fiscal year.

(e) "Assessed value" means the assessed value of real property that was used to determine the annual tax, and which is not reduced by any exemption from real property taxes. For real property classified as class two or class four real property, as defined in subdivision one of section eighteen hundred two of this article to which subdivision three of section eighteen hundred five of this article applies, unless other- wise provided, the assessed value is the lower of the actual assessed value and transitional assessed value.

(f) "Assessed value attributable to improvements" means that portion of the assessed value that was used to determine the annual tax attrib- utable to improvements, and which is not reduced by any exemption from real property taxes.

(g) "Improvements" means buildings and other articles and structures, substructures and superstructures erected upon, under or above the land, or affixed thereto, including bridges and wharves and piers and the value of the right to collect wharfage, cranage or dockage thereon.

(h) "Physical decrease" means the decrease in assessed value from the assessed value on the preceding assessment roll as a result of destruction of property caused by the severe storm that occurred on the twenty-ninth and thirtieth of October, two thousand twelve, such decrease to which subdivision five of section eighteen hundred five of this article applies.

(i) "Physical increase" means the increase in assessed value from the assessed value on the preceding assessment roll as a result of an addi- tion to or improvement of existing real property as provided in subdivi- sion five of section eighteen hundred five of this article, for the purpose of reconstruction or repair in connection with the damage caused by the severe storm that occurred on the twenty-ninth and thirtieth of October, two thousand twelve, such increase to which subdivision five of section eighteen hundred five of this article applies subject to the provisions of this section.

(j) "Total square footage of the improvements on the property" means, with respect to an assessment roll, the square footage used by the assessor in determining the assessed value attributable to improvements on the real property for such assessment roll.

(k) "Transitional assessed value" is the transition assessment calcu- lated pursuant to subdivision three of section eighteen hundred five of this article, and which is not reduced by any exemption from real prop- erty taxes. 3. Affected real property. For purposes of this section, "affected real property" means any tax lot that contained, on the applicable taxa- ble status date, class one, class two or class four real property as such class of real property is defined in subdivision one of section eighteen hundred two of this article, as to which:

(a) the assessor reduced the assessed value attributable to improvements on the property for the assessment roll completed in two thousand thirteen from the assessed value attributable to improvements on the property for the assessment roll completed in two thousand twelve as a result of damage caused by the severe storm that occurred on the twenty-ninth and thirtieth of October, two thousand twelve; and

(b) the assessor increased the assessed value attributable to improvements on the property by means of a physical increase for an assessment roll completed from two thousand fourteen through two thousand twenty. 4. Limitation on increases of assessed value. Notwithstanding subdivision five of section eighteen hundred five of this article and any other provision to the contrary, increases in the assessed value of affected real property shall be limited in the manner specified in this subdivision.

(a) Except as provided in paragraph (c) of this subdivision, for affected real property for which the assessed values on the assessment rolls completed in two thousand fourteen and two thousand fifteen do not reflect a physical increase, the amount of the aggregate physical increase shall not exceed the amount of the physical decrease reflected in the assessed value on the assessment roll completed in two thousand thirteen. Any increase in assessed value from the preceding year in excess of the physical increase reflected in the current assessed value, such physical increase limited as provided in the preceding sentence, shall be subject to the limitations on increases provided in subdivisions one, two and three of section eighteen hundred five of this article. In no event shall the assessed value of the affected real property appearing on an assessment roll completed for any given year from two thousand fifteen to two thousand twenty exceed what the assessed value would have been that year but for any physical decreases or physical increases reflected in the assessed values on the assessment rolls completed from two thousand thirteen to two thousand twenty.

(b) For affected real property for which the assessed value on the assessment roll completed in two thousand fourteen or two thousand fifteen reflects a physical increase, the assessed value as it appeared on the assessment roll completed in two thousand fifteen shall be recalculated as if the limitation in paragraph (a) of this subdivision had been in effect for the assessment rolls completed in two thousand fourteen and two thousand fifteen. The recalculation of the assessed value that appeared on the assessment roll completed in two thousand fifteen shall not affect the amount of taxes that were due and payable for the fiscal year beginning on the first of July, two thousand fourteen. The assessed value on the assessment rolls completed for each of the years from two thousand sixteen to two thousand twenty shall be subject to the limitation on increases provided in paragraph (a) of this subdivision. Notwithstanding any provision to the contrary, the assessor is authorized to correct as provided in this paragraph the assessed value of affected real property appearing on the assessment roll completed in two thousand fifteen. Such correction shall be made no later than ninety days after the effective date of a local law adopted in accordance with this section.

(c) Notwithstanding paragraphs (a) and (b) of this subdivision, in the event that the total square footage of the improvements on the affected real property appearing on any assessment roll completed from two thousand fourteen to two thousand twenty exceeds the total square footage of the improvements on the property appearing on the assessment roll completed in two thousand twelve, the amount of the aggregate physical increase shall not exceed the amount computed by multiplying the sum of the physical increases as calculated subject to this subdivision by a fraction, the numerator of which is equal to the amount of the total square footage of the improvements on the property for the current assessment roll, and the denominator of which is equal to the amount of the total square footage of the improvements on the property for the assessment roll completed in two thousand twelve. For purposes of this paragraph, if improvements on the property located below grade were not included in the total square footage of the improvements on the property for the assessment roll completed in two thousand twelve, such improvements shall not be included in the total square footage for subsequent assessment rolls if the improvements were moved above grade or other building elevations were constructed on the property to prevent or mitigate flooding as part of reconstruction or repair in connection with the damage caused by the severe storm that occurred on the twenty-ninth and thirtieth of October, two thousand twelve.