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  11:57:29 pm on November 22nd, 0000   [ 091122  23:57:29 ].

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

Count 

online calc
normal depth critical depth discharge in culvert critical slope normal and critical depth tractive force
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 discharge sluice discharge weir discharge channel initial sequent HJ
critical constriction efficiency HJ ogee spillway Hazen-Williams parallel pipes three reservoirs
Creager rational slope-area linear reservoir storage indication 1 storage indication 2
Muskingum Muskingum-Cunge time-area Clark UH cascade of linear reservoirs
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
convolution S-hydrograph time of concentration
UH cascade dimensionless UH cascade general UH cascade series UH cascade all series UH cascade
hyperbolic regression one-predictor linear one-predictor nonlinear two-predictor linear two-predictor nonlinear
fall velocity Lane & Koelzer USLE USLE2 Dendy-Bolton Shields
Duboys Meyer-Peter Modified Einstein Colby 1957 Colby reservoir design life
DO sag DO sag analysis Oxygenation Salinity (EC to TDS)