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A total number of 505 runoff episodes during SCPs were identified. Variable statistics for the episodes are summarized in Table 4. The statistical analyses indicated that some of the independent variables were correlated. After rejecting the highly correlated variables, the total number of variables in the model was reduced from 17 to 10. The stepwise regression resulted in the following linear relationship:

(1)

where Q_max is the maximum runoff (mm/h), RT is the roof type (0 for REF and 1 for green roof), P_max is the maximum precipitation intensity (mm/h),

and

is the maximum and minimum air temperatures, respectively (°C),

is the minimum snow depth (cm), and dh is the reduction in snow depth snow during the episode (cm). The

and

for Equation () were both 0.72 and all variable coefficients were significant.

Table 4

Variables used to predict and explain the maximum runoff from the roofs

Variable	Symbol	Unit	Min.	Median	Mean	Max.
Maximum runoff intensity	Q_max	mm/h	0.1	0.6	1.0	6.5
Episode duration		h	2	17	37	331
Total precipitation		mm	0.0	0.5	7.4	72.3
Precipitation as snow		mm	0.0	0.0	1.2	14.6
Precipitation as rain		mm	0.0	0.4	6.1	69.7
Maximum precipitation intensity		mm/h	0.0	0.3	1.0	6.8
Mean precipitation intensity		mm/h	0.1	0.6	0.6	1.6
Precipitation duration		h	0	2	11	139
Mean air temperature		°C	−6.8	2.6	2.8	14.5
Minimum air temperature		°C	−8.0	0.0	0.5	12.0
Maximum air temperature		°C	−6.0	4.7	4.9	16.1
Mean air temperature 24 h before		°C	−7.8	0.3	0.4	8.3
Mean air temperature 48 h before		°C	−6.4	0.1	0.1	8.1
Mean snow depth		cm	0	9	14	64
Minimum snow depth		cm	0	7	12	64
Maximum snow depth		cm	1	12	15	64
Reduction in snow depth		cm	0	1	3	34

Variable	Symbol	Unit	Min.	Median	Mean	Max.
Maximum runoff intensity	Q_max	mm/h	0.1	0.6	1.0	6.5
Episode duration		h	2	17	37	331
Total precipitation		mm	0.0	0.5	7.4	72.3
Precipitation as snow		mm	0.0	0.0	1.2	14.6
Precipitation as rain		mm	0.0	0.4	6.1	69.7
Maximum precipitation intensity		mm/h	0.0	0.3	1.0	6.8
Mean precipitation intensity		mm/h	0.1	0.6	0.6	1.6
Precipitation duration		h	0	2	11	139
Mean air temperature		°C	−6.8	2.6	2.8	14.5
Minimum air temperature		°C	−8.0	0.0	0.5	12.0
Maximum air temperature		°C	−6.0	4.7	4.9	16.1
Mean air temperature 24 h before		°C	−7.8	0.3	0.4	8.3
Mean air temperature 48 h before		°C	−6.4	0.1	0.1	8.1
Mean snow depth		cm	0	9	14	64
Minimum snow depth		cm	0	7	12	64
Maximum snow depth		cm	1	12	15	64
Reduction in snow depth		cm	0	1	3	34

Note: Observations are from the 505 episodes. Details on each variable is presented in ‘Methods’. Equation (1) is valid for the observations in the table.

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