presentation - precipitation - rain guage network

7/28/2019 Presentation - Precipitation - Rain Guage Network

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Precipitation Gauge Network Precipitation varies both in time and space

Sound hydrologic/hydraulic designs require adequate

estimation of temporal/ spatial precipitation patterns.

The density of rain gauge network depends on

(1) purpose of the study;

(2) geographic configuration of the study region;

(3) economic consideration.


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Rain Gauge Density in HK

Rain gauge density in HK is: Daily 13.6 km2/gauge

Autographic/ Automatic 11.0 km2/gauge

Rain gauge density is significant higher in Hong Kong Island and

much sparse relatively in New Territory (see figure).

Type Number of Stations Location Map

HKO Automatic Weather Station Rain Gauges 18 Figure 2

GEO Rain Gauge Stations - Telemetered 86 Figure 2

DSD Rain Gauge Stations - Telemetered 9 Figure 2

HKO Conventional Rain Gauge Stations 51 Figure 3

HKO Automatic Reporting Rain Gauges 21 Figure 2


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Conventional Raingauge Locations in HK


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Telemetered Raingauge Network in HK


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World Meteorological Organization (WMO)Suggestion

A minimum density for precipitation gauge network: (at least 10% are

automatic recording gauges)

I: Flat region of temperature, Mediterranean & tropical zones;

IIa: Mountain region of temperate, Mediterranean & tropical zonesIIb: Small mountains island with very irregular precipitation requiring

very dense hydrographic network

III: Arid and polar zones


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Errors Precipitation Measurement

1. Human Error: scale reading & water displacement (if adip stick is used)

2. Instrumental Defect: water to moisten the gauge; speed at

which mechanical devices work (such as tipping bucket

gages); & inadequate use of wind shield3. Improper Siting: height above ground of the gage orifice;

exposure angle; & regionalization techniques

(Ref: Uncertainties in Estimating the Water Balance of Lakes,

by T. C. Winter, Water Resources Bulletin, AWRA, 17(1),1981)


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Effect on Wind on Precipitation Measurement


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Analysis of Temporal Distribution ofRainstorm Event

- Only feasible for data obtained from recording gauges.

- Rainfall Mass Curve: A plot showing the cumulative rainfalldepth over the storm duration

- Rainfall Hyetogragh (/): A plot of rainfall depth orintensity with respect to time

- Instantaneous Rainfall Intensity,

(slope of the mass curve)

- Average Intensity in (t, t + t) is

Time

Time

dt

dP(t)i(t)

t

tPttP

t

P

it

)()(


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Rainfall

Mass Curve&Hyetograph


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Autographic Chart


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Clock-Time vs. Rolling-Time Max Rainfall

Example (GEO Raingage N17 on 5 November 1993)

Time 15-min 5-min

Rainfall (mm) Rainfall (mm)

3:45

3:50 9.0

3:55 12.54:00 35.0 13.5

4:05 17.0

4:10 14.5

4:15 37.5 6.0

4:20 5.0

4:25 5.04:30 14.5 4.5

Clock-time 15-min maximum rainfall depth = 37.5 mm

Rolling-time 15-min maximum rainfall depth = 45.0mm


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Example of Rainfall Analysis


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Double Mass Analysis

Changes in gage location, exposure, instrumentation, or observational

procedures may cause relative change in the precipitation catch. Thisinformation is not usually included in the published records.

Doublemass curve analysis tests the consistency of the record at a gage

by comparing its accumulated annual or seasonal precipitation with the

concurrent cumulated values of mean precipitation for a group ofsurrounding stations.

Abrupt changes or discontinuities in the resulting mass curve reflect some

changes at the target gage. Gradual changes in the slope of the mass curve

reflect progressive changes in the vicinity of the target gage, such as thegrowth of trees around a rain gage.

The slopes of different portions of the mass curve can be used as a basis

for correcting the record of the target gage.


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Operation of Double Mass Analysis

Pi,t

or Pi,t

/ n

Px,t

Adjustment factor for dataafter 1916 = S1 / S2 , i.e.,

Px, t = Px, t S1/S2 , t > 1916

S2

S1

1916

A change of slope should not be considered significant unless it persists for

at least 5 years.

Due to the fact that the data may have some scatter, an indicated change in

slope should be confirmed by other evidence unless the change in slope is

substantial (say, greater than 10%).


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Example Double

MassAnalysis


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Point Rainfall Analysis

Purposes: To transfer rainfall amounts observed from nearby index

stations to ungauged location or gauge with missing data

Methods:

- Arithmetic average method

- Normal ratio method

- Inverse distance method (& modified versions)

- Linear programming & other optimization methods

- Isohyetal method

- Kriging method

General philosophy:

where ; Px = rainfall amount to be estimated ; Pi = rainfall

amount at index station i ; ai = weighting factor for index station i .

Sometimes, we may want to impose ai 0 for all i = 1, 2, n

n

1i i

P

i

aPx

1an

1i

i

Px?

P2

P1

P3

P4


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Arithmetic Average/Normal Ratio Methods

Arithmetic Average Method:

Normal Ratio Method:

or

where Ni = Average annual total rainfall at station i.

n

1i

ix Pn

1P

n

1i

iN

iP

n

1

N

P

x

x

n

1iiP

iN

xN

n

1

xP

1

n

1ii

a;

i

N

xN

n

1i

a


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Inverse Distance Method

Inverse Distance Method:

, i = 1, 2, , n

where Di = distance from index station i to the

point of estimation.

Issue: How to determine the "best" value for "b"?

n

1j

b

j1/D

bi

1/D

ia

Px?

P2

P1

P3

P4


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Modified Methods

Modified Normal Ratio Method:

i = 1, 2, , n

Issue: How to determine the "best" value for "b"?

Modified Inverse Distance Method:

i = 1, 2, , n

where Ei = elevation difference between the i-th index station and

the point of estimation.

a,b = constant

Issue: How to determine the "best" values for "a" and "b"?

n

1j

b

j1/D

i/N

xNb

i1/D

ia

n

1j

b

j

Ea

j

D

bi

Eai

D

ia


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Optimization Methods

Minimize (Min. Absolute Deviation, MAD, Criterion)

Subject to

ai 0, i = 1, 2, , n; Uj, Vj0, j =1, 2, , J

where Pij = rainfall amount for the j-th storm event at the i-th index station;

J = total number of storm events;

Uj, Vj = over- and under-estimation for event j

The above MAD objective function can be replaced by the least square criterion as

Minimize

Any other goodness-of-fit criteria we can use?

J

1jj

Vj

U

xjP

jV

jU

ijP

n

1ii

a

1n

1ii

a

J

1j

2j

V2j

U


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Isohyetal/ Kriging Methods

Isohyetal Method:

Estimate point rainfall depth by first construct equal rainfallcontour map (see HK annual total rainfall isohyetal maps)

Kriging Method:

- A geostatistical method originally developed in mining

engineering by Krige.

- The method is appropriate for dealing with random field

having non-repeated observation at different locations in

space.

- Preserve the spatial correlation structure of observed data.- Optimal weight factors, ais , are determined to minimize

the mean-squared-error at the point of estimation.

- The by-product of the method is to produce error map of

estimation.


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Areal Rainfall Analysis

n

1i

ii PaP

Rainfall gauges provides point measurements of rainfall amount (in terms

of depth). In some hydrologic applications, spatial variation or averagedepth of precipitation over a given area is needed.

Equivalent Uniform Depth (EUD): Depth of water that would result if all

of the precipitation received were uniformly distributed over the designated

area.

Methods for Estimating Mean Areal Rainfall:

- Basic Idea :

where P = EUD ; Pi = rainfall depth at station i ;

ai = weighting factor for station i , 0 ai 1 , and

n = total number of stations (or gauges)


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Arithmetic Average Method :

where n = number of rain gauges within the designated area.

Thiessen Polygon Method:

Attempt to define the area represented by each gage in order to weigh the

effects of non-uniform rainfall distribution.

Procedure :(1) Connecting lines of gages are drawn.

(2) Draw perpendicular bisectors of these connecting lines.

(3) Determine the area of each polygon , Ai , where = total area

of interest

(4)

Limitations :

(1) Inflexiblenew polygon is needed if there is any change in the

number of gages or the position of gages.

(2) Does not consider orographic influences.

Arithmetic Average/Thiessen Polygon Methods

n

1iiP

n

1P

An

1ii

A

i

i

P

n

1iia

n

1iiPA

iA

A

iPi

A

P


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Isohyetal Method/Others

Isohyetal Method

The method is generally considered to be the most accurate scheme

to compute the EUD of rainfall over a drainage area. Procedure :

(1) Contours of equal precipitation (isohyet) are constructed.

(2) Areas between successive isohyets are measured, Ai.

(3) Average precipitation depth between isohyets are computed, Pi.

(4) The basinwide EUD of rainfall is

The procedure is subjective in the sense of interpolating precipitation depth

between gages. Usually, linear interpolation is used. The accuracy of the

analysis heavily depends on the analysts skill.

Other Methods:

Trend Surface Analysis, Kriging Method, Hypsometric Method (see Shaw,

1994, p.211), and Multiquadric Method (see Shaw, 1994, p.212).

iP

ia

iP

A

iA

A

iPi

AP


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Examples


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Depth-Area Relation

Area (km2) 25 50 100 200

ARF 1.00 0.96 0.91 0.85

The DAD analysis is devised to determine the greatest precipitation

amounts for various size areas and durations over different regionsand for certain seasons. The resulting DAD relationship is primarily

to be used for determining a hypothetical storm event for designing

hydraulic structures.

Area-Reduction Factor (ARF):

Allow estimating areal EUD of rainfall from point rainfall.

For Hong Kong, a recommended ARF values are (Task 2 Report

Territorial Land Drainage & Flood Control Strategy Study: Phase I,

1989, by Mott MacDonald HK Limited for HKSAR Drainage

Services Department)


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DAD Reduction Relations

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