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.
Rain Gauge Density in HK
Rain gauge density in HK is:
 Daily
 Autographic/ Automatic
13.6 km2/gauge
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
Conventional Raingauge Locations in HK
Telemetered Raingauge Network in HK
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 zones
IIb: Small mountains island with very irregular precipitation requiring
very dense hydrographic network
III: Arid and polar zones
Errors Precipitation Measurement
1. Human Error: scale reading & water displacement (if a
dip 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 shield
3. 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)
Effect on Wind on Precipitation Measurement
Analysis of Temporal Distribution of
Rainstorm Event
- Only feasible for data obtained from recording gauges.
- Rainfall Mass Curve 累積曲線: A plot showing the cumulative rainfall
depth over the storm duration
Time
- Rainfall Hyetogragh (組体圖/過程線): A plot of rainfall depth or
intensity with respect to time
- Instantaneous Rainfall Intensity,
(slope of the mass curve)
i(t) 
dP(t)
dt
- Average Intensity in (t, t + t) is it 
Time
P P (t  t )  P (t )

t
t
Rainfall
Mass Curve
&
Hyetograph
Autographic Chart
Clock-Time vs. Rolling-Time Max Rainfall
Example (GEO Raingage N17 on 5 November 1993)
Time
3:45
3:50
3:55
4:00
4:05
4:10
4:15
4:20
4:25
4:30
15-min
Rainfall (mm)
5-min
Rainfall (mm)
35.0
37.5
14.5
 Clock-time 15-min maximum rainfall depth = 37.5 mm
 Rolling-time 15-min maximum rainfall depth = 45.0mm
9.0
12.5
13.5
17.0
14.5
6.0
5.0
5.0
4.5
Example of Rainfall Analysis
Double Mass Analysis
 Changes in gage location, exposure, instrumentation, or observational
procedures may cause relative change in the precipitation catch. This
information is not usually included in the published records.
 Double–mass 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 of
surrounding 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 the
growth 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.
Operation of Double Mass Analysis
 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%).
Px,t
S2
1916
Adjustment factor for data
after 1916 = S1 / S2 , i.e.,
Px, t = Px, t  S1/S2 , t > 1916
S1
Pi,t or Pi,t / n
Example –
Double
Mass
Analysis
Point Rainfall Analysis
· Purposes: To transfer rainfall amounts observed from nearby index
stations to ungauged location or gauge with missing data
P4
· Methods:
P1
- Arithmetic average method
Px?
- Normal ratio method
- Inverse distance method (& modified versions)
- Linear programming & other optimization methods
P3
P
2
- Isohyetal 等雨線 method
- Kriging method
n
· General philosophy: Px   a i Pi
i 1
n
where  a i  1 ; Px = rainfall amount to be estimated ; Pi = rainfall
i 1
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
Arithmetic Average/Normal Ratio Methods
 Arithmetic Average Method:
1
Px 
n
n

i 1
Pi
 Normal Ratio Method:
Px
1 n Pi


Nx
n i 1 N
i
or
1 n  N x
P 

x n

i  1  Ni

P
 i

where Ni = Average annual total rainfall at station i.


N
n
1
a 
x ;  a  1
i
 i

n N
i

1
i


Inverse Distance Method
• Inverse Distance Method:
a 
i
1/D i 
P4
P1
Px?
b
b , i = 1, 2, …, n
n 

 1/D j 

j  1
P2
where Di = distance from index station i to the
point of estimation.
Issue: How to determine the "best" value for "b"?
P3
Modified Methods
• Modified Normal Ratio Method:
a
i

1/D  b N /N 
i
x i

b
n 

 1/D j 

j  1
i = 1, 2, …, n
Issue: How to determine the "best" value for "b"?
• Modified Inverse Distance Method:
D  a E  b
i
i
a 
i
n
 D  a E  b
j
j
j 1
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"?
Optimization Methods
J
Minimize   U  V  (Min. Absolute Deviation, MAD, Criterion)
j
 j
j 1
n
Subject to  a P  U  V  P
i ij
j
j
xj
i 1
n
 ai  1
i 1
ai  0, i = 1, 2, …, n; Uj, Vj  0, 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
J
Minimize   U 2j  Vj2 


j 1
Any other goodness-of-fit criteria we can use?
Isohyetal/ Kriging Methods
• Isohyetal Method:
Estimate point rainfall depth by first construct equal rainfall
contour 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, ai’s , 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.
Areal Rainfall Analysis
• Rainfall gauges provides point measurements of rainfall amount (in terms
of depth). In some hydrologic applications, spatial variation or average
depth 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 :
n
P   a i Pi
i 1
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)
Arithmetic Average/Thiessen Polygon Methods
n
• Arithmetic Average Method : P  1  P
i
n
i 1
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.
n
(3) Determine the area of each polygon , Ai , where  Ai  A = total area
i 1
of interest
(4) P   AiPi  n  Ai  P  n a P
i
A
  i
i  1 A 
i 1
i
i
· Limitations :
(1) Inflexible – new polygon is needed if there is any change in the
number of gages or the position of gages.
(2) Does not consider orographic influences.
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 basin–wide EUD of rainfall is
A P
 Ai 
i
i
 P  a P
P
 
i i
 A i
A


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 analyst’s skill.
Other Methods:
Trend Surface Analysis, Kriging Method, Hypsometric Method (see Shaw,
1994, p.211), and Multiquadric Method (see Shaw, 1994, p.212).
Examples
Depth-Area Relation
• The DAD analysis is devised to determine the greatest precipitation
amounts for various size areas and durations over different regions
and 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)
Area (km2)
ARF
25
50
100
200
1.00
0.96
0.91
0.85
DAD Reduction Relations