Probabilities Flashcards
Exactly r times in n years
(n/r)p^r(1-p)^n-r
At least once in n years
1-(1-p)^n
Not occurring in n years
1-(1-(1-p)^n)
Trapezoidal Rule
Vi = ((Q1+Q2)/2)*(t2-t1)
H > UH
Write time and runoff flowrates (-baseflow)
Determine rainfall excess (-losses) (if different to uniform rain, use Phi-index to determine losses)
Scale q by rainfall excesses
Rainfall event procedure
Determine UH flowrates
UH > H
Write time and runoff flowrates
Set up table for rainfall events (r1UH, r2UH…)
Align rainfalls with starting time of events
Multiply UH by event rainfall starting with UH1, start multiplication where event starts!
Sum columns for UH
Multiply by net rain (-losses)
Add baseflow
To Produce S-curve
To Change an S-curve
[Time][UH][Lagged by D1 (x times until S values level out)][S curve (addition of UH to Laggedn columns)]
[Lagged S curve (by target D2)][Difference (Lag S - S)][UH D2 ((D1/D2)*diff)]
Superposition Procedure
For short to long D>nD n=integer
Lag identical UH by D1 x times (x=D2/D1 integer)
Sum columns for DRH runoffs
Divide DRH by x
[Time][UH][lagged UH][DRH][DRH/n]
UH Assumptions
Time invariant Linear response No baseflow Total volume (depth) = 1 unit (usually 10mm) Losses can be determined and seperated Rainfall uniformly distributed Rainfall intensity constant Superposition applicable
SV Equation
dv/dt + v dv/dx + g dh/dx - g(So-Sf) = 0
LA CA PF GF FF
Kinematic Wave SV Component
g(So-Sf) = 0
GF FF
Steady Uniform
Diffusion Wave SV Component
g dh/dx - g(So-Sf) = 0
PF GF FF
Dynamic Wave SV Component
dv/dt + v dv/dx + g dh/dx - g(So-Sf) = 0
LA CA PF GF FF
Unsteady Non-Uniform
Steady Non-Uniform SV Component
v dv/dx + g dh/dx - g(So-Sf) = 0
CA PF GF FF
Hydrological Cycle
Evaporation, transpiration, precipitation, run off, ground water
P-R-ET=0
Absolute Humidity
The mass of the water vapour per
unit volume of the moist air, in kg/m 3
Specific Humidity
The mass ratio between the water
vapour and the the moist air, in g/kg
Relative Humidity (%)
h = e / es % = water vap p / sat water vap p
Pyschometric Chart
(ew-e)=y(t-tw)
