onlineregression15:   Hyperbolic regression (intensity-duration regression)    ⇒   i = f(tr-1)

Formulas

1/i = (tr/a) + (b/a)              y = α + βx

α = b/a        x = tr        β = 1/a        y = 1/i

β = [Σ(xy)-(ΣxΣy)/n]/{Σ(x2)-[(Σx)2/n]}

α = [Σy-(βΣx)]/n

Reference

Ponce, V. M. 1989. Engineering Hydrology, Principles and Practices. Prentice Hall, pages 246-248.
Example
INPUT DATA:

Enter array size n:     

Enter paired values of arrays i and tr (separate each value with a comma; maximum string length is 300 characters).

i:      

tr:     

ECHO OF INPUT:

n =  

i(1) =  .   

tr(1) =  .   

OUTPUT:

a =            b =

            

  Your request was processed at  08:17:56 am on April 19th, 2025   [ 250419  08:17:56 ].

Thank you for running onlineregression15.   Please call again.   [070418]

Count 

online calc
normal depth critical depth normal and critical depth discharge in channel critical slope
normal depth in culvert critical depth in culvert discharge in culvert discharge sluice discharge weir
M1 wsprofile M2 wsprofile M3 wsprofile S1 wsprofile S2 wsprofile S3 wsprofile
C1 wsprofile H2 wsprofile A2 wsprofile C3 wsprofile H3 wsprofile A3 wsprofile
sequent depth HJ energy loss HJ initial sequent HJ efficiency HJ critical width constriction
ogee spillway Hazen-Williams parallel pipes three reservoirs tractive force
V-notch weir V-notch partially contracted Cipolletti weir Rectangular weir Standard contracted rectangular weir Standard suppressed rectangular weir
Froude number Vedernikov number Limiting contracting ratio
Creager rational slope-area linear reservoir storage indication 1 storage indication 2
Muskingum Muskingum-Cunge time-area Clark UH Cascade of linear reservoirs
USGS Methods for magnitude of floods in California Kinematic wave applicability Diffusion wave applicability Clark's unit hydrography compared to Ponce's version Correlation coefficient of a joint probability distribution Storage volume of a detention basin
Blaney-Criddle Penman Penman-Monteith reference crop Thornthwaite Priestley-Taylor Penman-Monteith ecosystems
Gumbel Gumbel 2 Log Pearson Log Pearson 2 TR-55 graphical curve number
Overland flow using the diffusion wave method Dynamic hydraulic diffusivity convolution S-hydrograph time of concentration water balance
UH cascade dimensionless UH cascade general UH cascade series UH cascade all series UH cascade
one-predictor linear one-predictor nonlinear two-predictor linear two-predictor nonlinear hyperbolic regression
fall velocity Lane & Koelzer USLE USLE2 Dendy-Bolton Shields
Duboys Meyer-Peter Colby 1957 Colby reservoir design life Equilibrium channel top width using the Lane et al. theory
Modified Einstein Procedure bridge scour using Melville equation
DO sag DO sag analysis Oxygenation Salinity (EC to TDS)