Hydrology II

research: investigation of rainfall processes, adequate representation of hydrologic processes over a range of scales, climatic and non-stationary analysis

application: lack of data, insufficient length of record, sensitivity analysis, long term simulation, substitution of design hyetograph

physically based vs statistical

temproal vs space-time

event based vs continuous

simulation vs forecasting

forecasting = real time prediction

prediction = simulation, frequency etc ???

efficient long term generation

robust models in all seasons and across a range of scales

convenient framework for analytical formulation of downscaling

combined use in real time prediction of rainfall

markov theory: modelling persistence and periodicity

point process theory: modelling random ocurence in time, reproducing clustering of cells

fractal theory: modelling rainfall process through preservation of its scaling properties

the poison process

rainfall is a random sequence of occurences in time (and space). the point process theory can model sequences of random occurences

advantages: analytical flexibility, cluster dependence, time and space domain analysis

Poisson process: P[N(0,t)=n]=((lambda*t)ⁿ*exp(-lambda*t))/n!

parameters: lambda: mean poisson arrival time

µ: mean intensity of a pulse, exp distributed

delta: mean duration of a pulse, exp distributed

advantage: analytically simple, analytical expression of DDFs

disadvantages: poorly representative

Parameters: lambda: mean poisson arrival time, mu: mean intensity of a call, delta: meand duration of a cell, beta: mean displacement of a cell from the cluster origin, nu: mean number of cells per cluster

model is more realistic than indep. rec. pulses model, but it underestimates short events.

sub-daily historical series

method of moments or max. likelihood

historical vs simulated storm profiles

historical vs simulated statistics

historical vs simulated extremes

internal storm properties: scaling, prob. funct, power sp...

--> use other timescales than used for calibration

use seasonal parameters (e.g. monthly) -> much better representation of extremes

parameter beta!

NSRP measures from the origin of the event

Bartlett-lewis measures between two successive cells

includes 2 types of rainfalls: stratiform and convective

solves the "overlappping problem" of stratiform and convective cells.

• traditional: point measurements
  • loss of information with respect to spacial (and temporal) variability
• advanced: measurements distributed in time and space
  • remote sensing

• rainfall
• soil moisture
• vegetation cover
• land use
• thematic maps

low penetration of the ground: ca 5-10 cm

RAdio Detecting And Ranging

1. emission and reception of el mag waves
2. backscattering from objects
   1. reflectivity (Z)
3. Z is dependent on Drop Seize Distribution (DSD)
4. Z is converted to precipitation depth

• to avoid inaccurate forecasting (due to inaccurate data base)
• understand processes
• build models
• verify modeling results

• reproduce nature's behavior
• maximise the efficiency of planning
• minimise the risk of failure
• analyse interaction with other systems

• detect moving weather systems
• estimates of 3D wind velocities

P = (CLZ)/r²

P: Backscattered Power, measured

C: Radar constant, data

L: fractal signal loss, measured

Z: radar reflectifity factor

r: range, data

ground clutter

erroneous echos (birds, airplanes)

shielding

ice, snow, rain

R = aZ^b

R: rainfall rate

a,b: parameters, event dependent

Z: reflectivity

• dependent on special var of process
• target of monitoring
• installation & maintenance costs

dense: short time, high var -> thunderstorms

sparse: long time scales, lim var -> general storms, annual average

bias: underestimation due to snow, ice

precision: random uncertainities due to the sparseness of network

conventional: stations/km2

optimisation methods: loss/gain criteria, bayes theorem