FS

runoff when rainfall intensity exceeds infliltration capacity

f(t) depends on soil properties, decreases over time

to compute f(t): richards eq, hortons, philips, green-ampt

time between beginning of rainfall until water starts ponding at the surface

correction for ponging time: f(t) is potential inf. rate, but if i<f(t) then it needs to be corrected:

integral f(t) from 0 to ts = i*tp

soil is saturated from below

already small rainfall intensities generate runoff

r=i if s=1

more widespread then inf exc mech

to predict where areas get satturated: topmodel/TI

sat hyd konductivity decreases exp with depth Ks(z) = K0*exp(-fz)

water table is parallel to the soil surface so that flow at point i is qi = T(zi)*tan(beta_i)

steady state conditins for recharge rate R to water table, locally aR = qi = T0 * tan(beta_i)*exp(-fzi)

saturation when zi < psi_c

ln(a/tan(beta)) > z_avg*f + lambda - psi_c*f

zi = z_avg-1/f*(ln(a/tan(beta))-lambda)

flow in subsurface is important for overall soil stability

geological: rock characteristics, weathering, bedrock structure

soil engineering: soil shear strength

geomorphic: slope gradient, slope shape, aspect, altitude, soil depth

hydrologic: precipitation, infiltration, soil water flow processes

vegetation

seismic + volcanic effects

-> factors can be predisposing or triggering

is f(nomal stress, cohesion, int angle of friction)

cohesion: true cohesion + apparent cohesion

true cohesion: bonding of particles

apparant cohesion: soil moisture, grain seizes, density, roots ....

shear strength of soil layer < shear stress on soil -> landslide, shear failure

assumption: H << L

if FS < 1 -> likely to fail

application: map susceptibility for landslides in space

most sensible parameters: h, H, u, (sat soil depth, total soil depth, pore water pressure)

shear strength of soil layer < shear stress on soil -> landslide, shear failure

assumption: H << L

if FS < 1 -> likely to fail

application: map susceptibility for landslides in space

most sensible parameters: h, H, u, (sat soil depth, total soil depth, pore water pressure)

used in infinite slope model

FS = soil strength/ shear stress = S/T = c/W*sin(beta)+tan(phi)/tan(beta)-u*tan(phi)/W*tan(beta)

increase slope angle

rise pore water pressure

rise in ground water level

reduced apparent cohesion

define a range of parameters and compute the probability P(Fs>1)

Monte Carlo analysis

SINMAP approach: wors case scenario SI > 1 if unconditionally stable (Fs_min>1)

best case scenario: SI = 0 if unconditionally unstable (Fs_max<1)

random scenario between SI = 0..1, SI = Pr(Fs>1)

for accuracy evaluation of predicted events

correct predicted safe, correct predicted unsafe

fals alarms, missed

comparison of efficiency, sensitivity, specificity, likelihood

graph for sensitivity, specificity, error I, error II

for different thresholds

the more bent the curve is, the better (less errors)

straight

braiding

meandring

anastomosing

-> are f(channel forming q, slope)

change from straight to braiding

with increasing slope, or increasing channel forming q

representative q that fundamentally shapes the channel

e.g. bankfull, mean anual flood etc

hortons law

basin shape

width function

order streams -> compute morphologic variables

Rb, Rl, Ra

Drainage density: D = L_T/A_{_Omega = 1/A_Omega * sum(N_omega*L_omega_avg)}

to quantify river morphology

relative distributing drainage area from the outlet.

if v=konst -> W(x) = distr of travel times in basin

for a given corss-section and changing discharge, channel geometry is fitted with the power law relations

(v=k*Qⁿ, w=a*Q^b d=c*Q^f)

for a given river system, channel geometry is fitted for discharge of the same frequency of occurence. often bankfull or mean annual discharge...

bankfull: flow that fills channel just to the top of the banks

most effective: flow that transports the most sediment on the long term

channel forming: flow that would form the same channel as the natural flow hydrograph does.

-> they can all be the same, but do not need to...

structures that have similar patterns/ geometric characteristics over a range of scales

objects with identical propery scaled parts are identical to the original, they are scale invariant

D= lim(log(N(r)/log(r)), r->0

D=0 point, D=1 line, D=2 area

in reality often 1.1...1.3

river network often have 2 dimensions: D≈1.1 -> shape of individual streams on small scale

D≈2 -> representing branching character of the network

can be expressed by hortons law: D = log(Rb)/log(Rl)

perfectly scaling (e.g. koch curve)

have a unique fractal dimension

are absolute scale free

have a scaling range where this relation holds

e.g. rivers, coastlines

to describe river network structure

identifying if (mean dissipation rate)/(unit channel) = konstant, if yes-> optimal

omega = tau * v = (rho*g*Sf*Q)/Pw = konst

erosion/depositon form channel in such a way that transport capacity is equal in the system (on the longterm).

-> equilibrium which is never reached but channels are adjusting towards it.

usefull to identify streams/ sections that deviate from the "optimal state"

belonging to the bank of a river

traditional semi-terrestrial areas

influenced by freah water, extending from the edge of water towards the edges of upland communities

very dynamic, e.g. clearance by flooding -> regrowth or not if to dry/wet etc...

abiotic + biotic env, lotic, lentic, semi-lotic

exchange of water, sediment, energy, nutrients on 4 dimensions

interconnected corridors

food webs, habitats

clustering + dispersion of populations

needs: flood disturbance -> cleaning & newly deposited sediment -> regeneration

hydrology: variability in flow

physical env: amont, variability

biology: diversity

water quality: temp. pH, BOD

geomorphology: eg. sediment load

regular low to medium flows: maintain water table -> growth

periodic high flows: channel movement + sediment deposition -> regeneration sites

well timed high + low flows: in growing season -> delivery of seeds -> establishment

gently traped flows after peak: sucessfull seed establishment (1-2.5 cm/d)

no high flows during sexond half of growing season: no destruction of seedlings

open sites: no competition for pioneers

moist enough: rooting of seeds

near to water: moisture + organis debris

different sediments: niches, variation