Examples
Examples
Try the starting example
- Elapsed infiltration observation times (hours)
- 0,1,2,3
- Measured infiltration rates (mm/hour)
- 50,24.7151776469,15.4134113295,11.9914827347
- Minimum decay k bound (per hour)
- 0.01
- Maximum decay k bound (per hour)
- 5
- Fitted initial rate f0 (mm/hour)
- 50
- Fitted asymptotic rate fc (mm/hour)
- 10
- Fitted decay k (per hour)
- 1
- Fit RMSE (mm/hour)
- 0
Try another scenario
- Elapsed infiltration observation times (hours)
- [1, 1, 2, 3]
- Measured infiltration rates (mm/hour)
- [50, 24.7151776469, 15.4134113295, 11.9914827347]
- Minimum decay k bound (per hour)
- 0.01
- Maximum decay k bound (per hour)
- 5
- Fitted initial rate f0 (mm/hour)
- 178.081427
- Fitted asymptotic rate fc (mm/hour)
- 11.359292
- Fitted decay k (per hour)
- 1.858298
- Fit RMSE (mm/hour)
- 8.939535
Calculation method
Calculation method
Fitted initial rate f0 (mm/hour)
Horton f(t)=fc+(f0−fc)e^(−kt), profile linear least squares in f0,fc at each k; bracket negative-to-positive profile-derivative zeros on64 bounded subintervals, refine roots, compare stationary candidates and bounds. Reject nonphysical fitted rates.
Fitted asymptotic rate fc (mm/hour)
Horton f(t)=fc+(f0−fc)e^(−kt), profile linear least squares in f0,fc at each k; bracket negative-to-positive profile-derivative zeros on64 bounded subintervals, refine roots, compare stationary candidates and bounds. Reject nonphysical fitted rates.
Fitted decay k (per hour)
Horton f(t)=fc+(f0−fc)e^(−kt), profile linear least squares in f0,fc at each k; bracket negative-to-positive profile-derivative zeros on64 bounded subintervals, refine roots, compare stationary candidates and bounds. Reject nonphysical fitted rates.
Fit RMSE (mm/hour)
Horton f(t)=fc+(f0−fc)e^(−kt), profile linear least squares in f0,fc at each k; bracket negative-to-positive profile-derivative zeros on64 bounded subintervals, refine roots, compare stationary candidates and bounds. Reject nonphysical fitted rates.
Symbols and units
- a
- Elapsed infiltration observation times (hours)
- b
- Measured infiltration rates (mm/hour)
- c
- Minimum decay k bound (per hour)
- d
- Maximum decay k bound (per hour)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- User-supplied measurements and assumptions; Bounded variable-projection least squares for Horton f(t)=fc+(f0−fc)e^(−kt); reject nonphysical fitted rates. Supported limits: Finite numeric values bounded to 1e9 magnitude; lists and tables contain 1–100 records unless a stricter bound is stated. Inputs use the units shown. Lists explicitly paired by a method must have matching lengths; independent polynomial coefficient vectors may differ. Respect stated physical, interpolation, policy and computational domain limits. At least three distinct observation times are required for a three-parameter fit; the scalar decay bound is finite and positive.
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These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.