Hydrology II
kärtchen für hydro II
kärtchen für hydro II
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?
- emission and reception of el mag waves
- backscattering from objects
- reflectivity (Z)
- Z is dependent on Drop Seize Distribution (DSD)
- 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)
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
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