On a long time perspective, the runoff rate is relatively constant (not to be mistaken for corrosion rate).

References
1 “Modelling and mapping of copper runoff for Europe”
I. Odnevall Wallinder, B. Bahar, C. Leygraf and  J. Tidblad Journal of Environmental Monitoring, 9, 66-73, 2007.
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2 "Predictive models of copper runoff from external structures"
I. Odnevall Wallinder, S. Bertling, X. Zhang, and C. Leygraf, Journal of Environmental Monitoring, 6, 704-712, 2004.
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3 "Long term corrosion-induced copper runoff from natural and artificial patina and its environmental fate" S. Bertling,
I. Odnevall Wallinder, D. Berggren and C. Leygraf, Environmental Toxicology and Chemistry, 25(3), 891-898, 2006.

www.corrosionscience.se

Scenario
! As an example, the predicted runoff rate of  g/(m2,year) is valid for a m2 copper roof, this equals  g of Cu released per day. If the predicted amount of copper runoff reaches a river that is m deep and m from one shore to the other with a water mass flow of  m/sec =  m3/day, the added copper concentration from the runoff water to the river is  µg Cu/L.
Copper released from tapwater systems in Stockholm: 4300 kg / year
Copper released from traffic in Stockholm: 5700 kg / year
CORROSION-INDUCED COPPER RUNOFF
FROM EXTERNAL CONSTRUCTIONS
Predicted runoff rate:  g/m2,year

! The total copper runoff rate is not a direct measure of any environmental effect.
 

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DIVISION OF CORROSION SCIENCE
THE ROYAL INSTITUTE OF TECHNOLOGY
WHAT IS COPPER RUNOFF?
Copper corrodes naturally outdoors forming a surface patina. Copper runoff is the amount of copper that can be released from the patina during rainfall.

HOW CAN COPPER RUNOFF BE USED?
It is important to assess the contribution of released copper from external constructions compared to other sources. Copper runoff is important key information to assess potential environmental effects. The chemical speciation and the bioavailability of released copper must also be considered.
Annual rain quantity
mm / year
pH
decades
S02- concentration
µg / m3
Angle of inclination
degrees

The annual rain quantity varies typically within the range of 400-3200 mm/year depending on geographical differences.

Stockholm, Sweden - 500 mm/year
Singapore, Singapore - 3000 mm/year
Davos, Switzerland - 1200 mm/year
more...

! Prevailing rain characteristics influence the runoff rate. For instance, high rain intensity usually means short contact time with the copper surface, which results in lower copper runoff and vice versa.

Rain pH is a measure of the rain acidity. The copper runoff increases with decreasing pH and vice versa.

pHStockholm, Sweden - pH 4.6
Singapore, Singapore - pH 4.4
Davos, Switzerland - pH 5.9
more...

! Rain pH is, for instance, influenced by acidifying pollutants such as H2SO4 and HNO3.

SO2 is a known gaseous pollutant that stimulates the corrosion of copper.

Stockholm, Sweden - 3 µg/m3
Singapore, Singapore - 22 µg/m3
Davos, Switzerland - 1.3 µg/m3
more...

! The SO2-concentration is often reported in parts per billion, ppb. 1 µg/m3 = 2.64 ppb

The degree of inclination from the horizontal largely affects the runoff process. The runoff depends on the projected area onto which a given rainfall volume impinges.

! It should be noted that the model implies no runoff from a vertical façade (α = 90°). This may not be true at real conditions due to the effect of prevailing wind conditions (not considered in the model), construction geometry and sheltering effects.