What Site Characteristics Explain Variability Of Peak Footing Drain Flows? Oskar Nordstrom, P.E. Mark TenBroek, P.E. CDM Michigan Inc. Ann Arbor, MI MWEA Annual Conference June 22, 2009
City of Ann Arbor Community Background 40 mi 2 sewer area, Population 114,000 Over 22,072 residential structures Originally 12,253 with active footing drains 1999 detailed studies, including SWMM analysis 5 problem neighborhoods 5% of city area 50% of backups 70-90% of peak flow from private sources 2001 - City FDD ordinance Established program and funding Over 1,400 FDDs completed About 250 FDDs/year
FDD Work Single Family Homes Reroute footing drains to sump near sanitary lead connection Sump pump drainage piping discharged outside Curb Drain Collection Deal with nuisance flows Minimally invasive horizontal directional drilling
Sump Pump Monitoring 60+ single family homes monitored Mostly in study areas 5 multi-family Representative Rain Gauges Mostly WWTP & Airport Converted to 15 minute precipitation
Data Analysis Goals Estimate peak footing drain flows MDEQ design standard (24 hr - 25 year event) Determine how peak flows affected by: Rain event characteristics Seasonality Establish site characteristics that affect the peak footing drain flows Contribution to I&I Base Model -> Site Specific Inclusive Model
Event Selection Selected events with following criteria: Larger events: > 1.25 inches over 24 hours High intensity events: > 0.75 inches in 1 hour > 0.50 inches in 15 minutes Selected 32 events based on total 24 hour precipitation
Peak 30-min Flow (gpm) 0 5 10 15 Peak 30-min Flow Responses Peak 30-min Flow vs 24 Hour Precipitation 0 1 2 3 4 24 Hour Precipitation (in)
Monitor Peak Flow Characteristics Large Variability ~0 to 15+ GPM Few homes with large peaks raise the average HIGH value in finding high producers
Potential Site Factors All available in digital format Started out with about 40 characteristics GIS Topography: Elevation and Slopes within 250 ft. of house 750 ft. of house 1500 ft. of house Soils - Permeability, type, description etc.
Potential Site Factors (Continued) City Databases Construction Era Year house constructed Grouped by house and connection types from field experience Basement Area Basement Perimeter
Developing a Site Factor Model Statistical Multiple Regression Model Base Model Flow ~ f(precipitation) β is the response slope; E is the error; and β 0 the intercept Site Factor Model Flow ~ f(precipitation, Site Factors)
Statistical Model Development Factor Correlation Matrix Identify and remove redundant factors Iterative Reduction Method Changes in R 2 Akiake Information Criterion (AIC) balances value to complexity Started out with an all inclusive model Flow ~ (β N x Factor N ) x Rain + Error Reduced by 1 low impact factor each cycle
Site Factor Findings Hydrologic Soil Group C and D = higher footing drain peak flow B = lower peak footing drain flow A = not enough data Construction Era/Type 1965-1981 highest peak flows Colonial style homes lower peak flows Small variations among other groups
Site Factor Findings (Continued) Elevations 250 ft & 750 ft distance both important - Higher surrounding area = Higher peak flows 1,500 ft distance not significant Mean Slope Higher = Lower peak flows Basement Area Smaller Basement = Higher peak flows Permeability Top layer of soil more porous = Higher peak flows
Site Factor Model 30 Minute Peaks Factor Contributions for 30 min Peak Flows Factor Default Minimum Mean Maximum Range Contribution Intercept 0.53 Basement Area -1.69-1.09-0.54 1.15 9% MeanElev - 250' -0.3 0.052 0.55 1.355 10% MeanElev - 750' -0.24 0.11 0.47 0.71 5% MeanSlope - 1500' -1.95-1 -0.35 1.6 12% Construction Era 0-2.69-0.53 0.32 3.01 23% HSG 0 0 0.76 2.53 2.53 19% Permeability 0 0 2.55 2.75 2.75 21% R 2 = 0.28 Site specific slope: 1.2 to 3.9 GPM peak 30 min flow / inch of rain
Next Step Apply approach citywide Sample Location Built 1963, Basement Area = 1,288 ft 2 HSG type B soil Top layer soil permeability = 1.2 inches/hour Mean Elevation 250 & 750 = 1.13 ft & 0.73 ft Mean slope within 1,500 = 4.9% Peak 30 min Flow = 0.61 GPM / Inch Rain Peak 3 hour Flow = 0.15 GPM / Inch Rain
Algorithm for Predicting Peak Flow Calculated the site specific response slope Sites grouped into top 25%, middle 50% and bottom 25%
Value of Method Determine neighborhoods that would likely yield higher peak flows Focus future FDD efforts in these areas Must be aware that FDD is most efficiently done in larger groupings Increases acceptability Better public engagement More efficient curb drainage systems
Weather Influences Antecedent rainfall volume Rain event characteristic Seasonality Snow pack Analysis now performed for each event Average flow adjusted for site factor influences Included monitors with valid data only
Antecedent Moisture Antecedent precipitation less important during growing season Antecedent precipitation less important the further before each event
Peak Flow (gpm) 0 1 2 3 4 5 Seasonality / Event Characteristics Event Average Peak Flow vs Total 24 Hour Precipitation by Season Dormant 30m Flow = 1.36 + 0.12 x Rain R2= 0 Growing 30m Flow = -0.43 + 1.41 x Rain R2= 0.43 0.0 0.5 1.0 1.5 2.0 2.5 3.0 24 Hour Precipitation (in)
Peak 1 Hour Precipitation (in/hr) 0.0 0.5 1.0 1.5 Event Characteristics Average Event Intensity vs Event Peak Hourly Intensity Dormant Season Growing Season 0.1 0.2 0.3 0.4 0.5 Average Hourly Precipitation During 24 Hour Period (in/hr)
Event Characteristics Summary Growing Season R 2 up to 0.65 Dormant Season R 2 down to about 0.10 Antecedent precipitation less important during growing season
Conclusion Method explains factors impacting the variability of peak footing drain flows Determined important factors Soil Characteristics, Relative Elevation, Construction (Age, Type, Method) Seasonality & rain event characteristics matter Can extrapolate to MDEQ remedial design standard Antecedent moisture important for growing season, much less important for dormant season Rain event characteristics (seasonality) impact observed peaks
Questions?
Initial Evaluations Calculated parameters Peak Flow at House / Average Event Flow Event Residuals Peak Flow / Precipitation Parameters plotted against all Site Factors Linear Regression R-squared Variability explained P-value Probability that relationship at least as extreme is explained by chance alone
Model Development Process Akaike s Information Criterion (AIC) Measures Information vs Complexity of Model Change (Difference) > 3 is significant Step 1 Model 1 = Starting Model Select Factor X usually lowest P value Model 2 = Model 1 less Factor X
Model Development Process Cont d Step 2 Compare R-squared Verify that change is significant Step 3 Compare AIC If change larger than 3 it is significant Lower number is better Step 4 Make Decision
Antecedent Conditions 4-, 2-, 1- week and 4 day, within event precipitation No linear relationship found Weakened the model Change to Categorical Variables Is the precipitation volume within prior timeframe larger than a certain volume (Yes or No)