Hydrology II

kärtchen für hydro II

kärtchen für hydro II

Christian Voegeli

Christian Voegeli

Set of flashcards Details

Flashcards 58
Language English
Category Nature Studies
Level Primary School
Created / Updated 15.10.2013 / 16.01.2017
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how to monitor?

traditional: point measurements

 - loss of information with respect to space variability

advanced: distributed in time and space

- remote sensing

how to monitor?

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

measurements are possible for:

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

problems of measurements by remote sensing:

low penetration of the ground: ca 5-10 cm

what does radar mean?

 

RAdio Detecting And Ranging

how does a weather radar work?

  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

why monitoring?

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

advanced methods in hydrology can....

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

what can the doppler effect be used for in remote sensing?

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

radar equation

P = (CLZ)/r2

P: Backscattered Power, measured

C: Radar constant, data

L: fractal signal loss, measured

Z: radar reflectifity factor

r: range, data

Errors in remote sensing

ground clutter

erroneous echos (birds, airplanes)

shielding

ice, snow, rain

rainfall estimation with radar:

R = aZb

R: rainfall rate

a,b: parameters, event dependent

Z: reflectivity

why dense or sparse raingauge network?

  • 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

problems of raingauges

bias: underestimation due to snow, ice

precision: random uncertainities due to the sparseness of network

 

criteria for raingauge network design

conventional: stations/km2

optimisation methods: loss/gain criteria, bayes theorem

how to improve accuracy of raingauges?

increase duration of measurements

increase number of stations

reasons for missing data

  • equipment failure
  • extreme events
  • human induced disturbances
  • mishandling of data records
  • accidental losses
  • limited resord length

3 approaches fo fill in missing data

classical: interpolation & weighing

regression: linear simple & multiple regression techniques

time-series analysis: linear stochastic models (most used to extend data records)

3 methods to estimate missing data with classical methods

station average method: take average of neighbouring stations

normal-ratio method: take average of neighbouring stations, weighted by theyr relative contribution

inverse distance weighing: weights neighbouring stationvalues by theyr distance. To avoid redundant information, the area should be devided into quarters and only one station per quarter should be considered.

estimating missing data by regression methods

linear regression

multiple regression

estimating missing data by regression methods:

- equation of simple lin regression

- how are parameters estimated?

y_t = a + b*x_t + alpha*......*e_t

where e_t = white noise, with amplitude alpha*....*...

a,b = population parameters of the regression

rho = popupation cross-correlation coeff; if rho = 1 or -1 -> perfect correlation, no noise

y_t = variable with missing data/ shorter record; dependent variable

x_t = variable with full data/ longer record; independent variable

- parameters are estimated from sample moments

 

what can a lin regression model with theta = 0/1 be used for?

theta = 0: no white noise, only a few records are missing

theta = 1: with withe noise, a significant number of missing records or extension of short records

problem with theta = 1 in a lin. regression model?

problem with theta = 0 ?

- the extended sequence is not unique, because of the randomly generated values of e_t

- underestimation of variance in the extended record. can be solved by using modified parameters a & b. (also for multiple regression)

equation for multiple regression

alpha = coefficient, f(record length, # of sites)

R = population multiple correlation coeff

 

how are a, b, R and sigma_y estimated in a multiple regression model?

a,b,R = estimated from sample moments

sigma_y = s1(y1), estimated from sample y_t of size N1

how can the efficiency of the extension from N1 to N1+N2 be assessed?

by evaluation the veriance of the mean computed from the extended data set N1+N2 as compared to that computed from the original data set N1.

is must be: var(y_mean(N1+N2)) < var(y_mean(N1))

-> critical correlation coeff  r=f(N1) can be formulated to ensure the condition above

what simple time series models do we know?

(P)AR(1): (periodic) autoregressive

-> can be used to fill in missing data when no nearby site with concurrent information is available.

MAR: multivariate autoregressive

-> for multiple sites, parameter estimation: least squares

 

what scales can the discussed models be used for?

up to the daily scale. for smaller scales use simulations (monte carlo) or synthetic data generation

 

are regression models sensitive to outliners?

yes

should the discussed models be applied for large gaps in records?

no, synthetic data gerenation is prefered

groups of disaggregation techniques

deterministic

stochastic

scaling

mixed

-> no universal technique available, many different approaches, often problem specific

rainfall disaggregation: constant model

rainfall is assumed to be constant over the timestep. all disaggregated intervals are wet and have the same intensity.

it is a deterministic model

ormsbee model

a deterministic model for rainfall disaggregation from 1h to 10min

geometric construction without parameter estimation

assumption:  the internal rainfall pattern is geometrically similar to the external pattern.

linear interpolation between 3 consecutive hourly rainfall amounts.

all 10' intervals are wet

pos: self-similar, only dataset needed

neg: no dry intervals, only for small scales

whats the aim of stochastic rainfall disaggregation methods?

preservation of the statistical features across scales

what is scaling?

what is self-invariance?

scaling: distribution remains the same on different scales -> self-similarity

self-invariance: lambdan = Zlambda_T(t)/ZT((t)

lambda = scaling factor, n = scaling exponent

 

what is the principle behind the cascade model approach?

to disaggregate low res data into higher resolution

branching mechanism, which distributs rainfall between the intervals of the successive cascade level

cascade model with branching nr 2

1. P(0/1), P(1,0), P(x,1-x)

2. Distribution of x/1-x

-> values can be obtained by aggregating existing data.

-> probabilistic nature of the approach = multiple solutions can be produced

-> -> for validation: take average of multiple realizations!

what is the difference between canonical and microcanonical?

canonical: preserves mass on average (over many samples/realisations); E(W) = 1; model has 2 parameters: beta & sigma2

microcanonical: preserves mass exactly; sum(W) = 1; model has 1 parameter: a

what is bounded and unbounded?

bounded: scale dependent, f(W) = f(W,lambda)

unboundend: scale independent; f(W) = f(W)

categories of rainfall models

physicaly based limited area models LAM

stochastic space-time models

statistical models