The Development of a Webbased Rainfall Atlas for Southern Africa

1
Title
The Development of a Web-based Rainfall Atlas
for Southern Africa
Günther Kratz, Walter Zucchini, Oleg
Nenadic, Institut für Statistik und Ökonometrie,
University of Goettingen, Germany.
2
toc
The Development of a Web-based Rainfall Atlas
for Southern Africa
contents
Development and Calibration of a daily rainfall
model Interpolation of the daily rainfall model
parameters Generating artificial rainfall
sequences Information transfer
3
Purpose
Purposes of the Rainfall Atlas
A water resources decision support system
4
1 dev/calib
i. Development and Calibration of a daily
rainfall model
Joint distribution of the rainfall amount for
site x

• discrete part (does it rain)
• continuous part (if it rains, how much?)

Sample observed daily rainfall amounts for site x.
5
1 discrete part
i. Development and Calibration of a daily
rainfall model

• discrete part of the daily rainfall model

• first-order (seasonal) Markov Chain with two
  states W (wet) and D (dry)

W
D
Observed daily rainfall amounts for a given site
Estimated probabilities and conditional
probabilities.
First-order Markov Chain

• Since pWpD1, pWWpDW1 and pDDpWD1
  it is sufficient to consider only pW , pWW
  and pWD

6
1 seas in discrete part
i. Development and Calibration of a daily
rainfall model

• seasonality of the discrete part

l(T)
e.g. pWD(T) (Probability that rain
occurs on period T ,given that T-1 was dry)
pgt0.5
0
plt0.5
Seasonality of the probability for a wet day
given that the day before was dry

• Instead of using 365 Parameters (probabilities
  are estimated for each day), an
  approximation with the first two terms of the
  Fourier Series representation is used.
• To avoid inadmissible estimates (estimated
  probabilities exceeding the interval 0,1)
  logits (llog(p/(1-p))) instead of probabilities
  are used.

7
1 continuous part
i. Development and Calibration of a daily
rainfall model

• continuous part of the daily rainfall model

Empirical distribution of rainfall-amount on
rainy days
Fitted Weibull distribution with Parameters a(T)
(scale parameter) and b (shape parameter)

• The mean m(T) exhibits seasonal behavior,
  while the CV remains constant

8
1 model summary
i. Development and Calibration of a daily
rainfall model

• the daily rainfall model

Parameters (discrete part)
seasonal
...
1
2
3
365
t
d
d
d
d
State 1 dry day
Discrete part
...
w
w
w
w
State 2 wet day
Amount of rainfall on wet days
Continuous part
...
Scale parameter seasonal
AMMU (0) AMMU (1) AMMU (2) PHMU (1) PHMU (2) CV
Parameters(continuous part)
Weibull Distribution
Shape parameter non-seasonal
9
2 interpolation
ii. Interpolation of the daily rainfall model
parameters
gradient
aspect
Parameters for the calibrates sites
roughness
Calibrated sites (5070)
kriging with externaldrift
exposure
Topological features
1.5 km
Interpolated parameters ...
... resulting in a resolution of 1 square mile
10
3 generating
iii. Generating artificial rainfall sequences
Artificial rainfall sequence (5000 yrs)
Model
16 Parameters
1,825,000 times(? 5000 years)
Empirical statistics (950)
Site x
Simulation for each of the 424,646 sites

• 1 GB zip-compressed ASCII-Files
• 950 statistics for each of the 425,000 sites

Database
11
4 inftrans
iv. Information transfer

• Image database

• data preparation

126x100 px
255x203 px
1065x842 px
443x355 px
693x550 px

• 5000 maps in 5 different sizes

• Site database

• Since information is required in two forms
  as maps (e.g. for ecologists) as well as in
  numerical form (e.g. for engineers) the
  database was used to construct an Image and a
  Site Database

• extraction of statistics for single
  sites into separate, small files

12
4 data struc
iv. Information transfer

• Data Structure

Mean SD CV
Percentiles Rain per Rainday
Stormdays Storm Percentage Stormrain
ANNUAL
1 5 10 25 50 75 90 95
99
Mean SD CV
Percentiles Rain per Rainday
Stormdays Storm Percentage Stormrain
Exc. prob.
MONTHLY
10mm 25mm 50mm 75mm 100mm 125mm
150mm 200mm
DAILY
Dry run probability
5 days 10 days 15 days 20 days 25
days 30 days
PARAMETERS
Cities Rivers Altitude
Max.mean Max.prob. Min.mean Max.mean
SI-mean SI-SD
OTHER DATA
13
4 image db
iv. Information transfer

• Image Database

Selection of the desired data types (according to
the scheme previously described)
The resulting maps are displayed in the lower
frame (with an option to view the maps in bigger
size)
14
4 image db
iv. Information transfer
4 site db

• Site Database

3.)
1.)
The site is selected either by clicking on the
imagemap or by entering coordinates.
2.)
PHP-Script
The required statistics can be selected via a
form-element.
The input is parsed to a PHP-script which reads
the appropriate data and displays the output in
tabular form.
Site database
15
summary
v. Conclusion

• It is shown, that it is possible to make a large
  repository of map- and numerical data
  available over the internet without
  heavyweight database-systems.
• Currently, work is done in creating a Java-based
  applet, which simulates rainfall-sequences
  (on annual, monthly or daily basis).
• Possibilites to expand the rainfall atlas to
  other countries are evaluated.
• Preliminary results are located on
  http//134.76.173.220/rainfall/ (feedback,
  critism and suggestions are welcome!)