8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.1
INTERDIURNAL AND INTERANNUAL VARIABILITY
IN STOCHASTIC DAILY WEATHER GENERATOR:
MODELLING AND THE ROLE
IN AGRICULTURAL AND HYDROLOGIC STUDIES
Martin Dubrovsky1, Josef Hejzlar2, Jan Kysely3, Josef Buchtele4,
Zdenek Zalud5, Daniel Marvan6
1
Institute of Atmospheric Physics AS CR, Hradec Kralove, Czech
Republic (CR)
2
Hydrobiological Institute AS CR and Faculty of Biological Sciences USB,
Ceske Budejovice, CR
3
Institute of Atmospheric Physics AS CR, Prague, CR
4
Institute of Hydrodynamics AS CR, Prague, CR
5
Mendel University of Agriculture and Forestry, Brno, CR
6
Faculty of Mathematics and Physics, Charles University, Prague, CR
this presentation:
home page:
e-mail:
www.ufa.cas.cz/dub/impacts/8imsc.doc
www.ufa.cas.cz/dub/dub.htm
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.2
Introduction
WGs are extensively used in climate change impact studies to provide
synthetic weather series representing present and changed climate
conditions. The series are used, e.g., as an input to:
 crop growth models
 hydrological rainfall-runoff models
quality of the weather generator (2 viewpoints):
1. statistician:
How do the synthetic series resemble the observed series ?
validation: (observed weather series) vs. (synthetic weather series)
answer: some properties are well reproduced, some only poorly
2. WG user: How do the imperfections affect results obtained by my
model (crop growth model, hydrological model)?
validation: distribution function of crop yields (streamflows, ...) simulated
with observed vs. synthetic weather series
answer: no effect / little effect / great effect
contents of this presentation:
(motivation:
- show that even “simple” weather generator may provide good service
- improve reproduction of interdiurnal and intermonthly variability
1. old version of WG - Met&Roll
2. demonstration of Met&Roll's performance
- validation of statistical structure
- usage in crop models and hydrological model
3. improved generator
4. demonstrating effect of the improvements
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.3
first version of Met&Roll
variables and model (~ WGEN):
variable
model
occurrence
Markov chain
(order=1)
π1, π01
[monthly]
amount
Gamma distribution
α, β
[monthly]
PREC
(precipitation)
parameters
SRAD (solar radiation)
A,B: 3x3 matrices
TMAX (max. temperature) AR model:
+ 3  (wet/dry) 
TMIN (min. temperature) x*(t+1) = Ax*(t) + Be (avg’s/std's)
AR(1) model: x*(t+1) = Ax*(t) + Be, where
x* 
x  m( x )
s( x )
where:
 m(x) , s(x) : depend on day of the year and precipitation occurrence
 A, B
: are constant
How do the synthetic series resemble the observed series ?
- parameters of WG are perfectly reproduced
insufficiencies:
- frequency of long dry spells is underestimated, especially in winter
- SRAD, TMAX, TMIN do not have normal distribution
- lag-0 and lag-1correlations have annual cycle [→ Fig. 1]
- variability of monthly and annual means is underestimated [→ Fig. 2]
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.4
Fig. 1. Lag-0 correlations among SRAD, TMAX and TMIN. (weekly;
calculated from the 30-year observed series. The vertical bars at the right part of
the graphs indicate the 95% confidence intervals of the all-year correlations).
Fig. 2. Reproduction of the variability of monthly and annual means by
Met&Roll. The figure displays the ratios of observed to synthetic sample
standard deviations of monthly and annual (Y) means of SRAD, TMAX, TMIN and
RAIN. The ratios were averaged over 17 stations in the Czech Republic.
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.5
How do the imperfections of the generator affect
results obtained in practical applications?
requirement: probability distributions of outputs of models feeded by
observed and synthetic weather series do not differ!
a) in crop growth modelling:
experiment: 30year simulation of crop growth with CERES-Wheat
input weather data: PREC, SRAD, TMAX, TMIN (daily characteristics)
30y observed vs. synthetic series (17 stations)
validation: - Wilcoxon test
- avg, std, quantiles of the 29 grain wheat yields [→Fig. 3]
results:
- only small differences between grain yields simulated with
observed and synthetic weather series;
- standard deviation is underestimated by 10%
- similar (slightly better) results for maize and spring barley
b) in hydrological modelling:
experiment: 39y simulation of rainfall-runoff regime in a river catchment
with Sacramento soil moisture accounting model (SAC-SMA;
= conceptual water balance model, Burnash 1995)
input weather data: TAVG and PREC (daily characteristics)
- 39y observed vs. synthetic weather series
validation:
a) monthly statistics (→Fig. 4)
- average flows are slightly underestimated in APR-JUN
- average monthly maxima are underestimated during greater part
of the year; largest misfit in APR-JUN + NOV
- variabiliy of monthly means and monthly maxima are
underestimated during whole year, by 50% in spring
b) distribution of streamflow averaged over 5 days (Fig. 5)
- frequency of high streamflows is underestimated if synthetic series
are used; greatest underestimation in spring
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.6
Fig. 3 Variability of model wheat yields simulated with observed and synthetic weather series.
left:
minimum, median and maximum values from 29y simulation
centre: ratios of averages and standard deviations obtained with the two weather series
right: Wilcoxon statistics for comparing distributions of the yields obtained with the two weather series
(values below zero indicate somewhat higher yields obtained with synthetic weather series)
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.7
Fig. 4 Averages [ AVG(...) ] and standard deviations [ STD(...) ] of monthly averages (left) and monthly
maxima (right) of daily stramflows. OBS = observed values; CB = simulated with observed weather series;
SYNT = simulated with synthetic weather series.
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.8
Fig. 5 Probability distribution of 5-day average streamflow [model
SACRAMENTO; Malse River; 39 years]
OBS = observed values
CB = simulated with observed weather data
SYN = simulated with synthetic weather data
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.9
Improvements of the generator's model
(with a stress on interdiurnal and intermonthly variability)
1. annual cycle of lag-0 and lag-1 correlations introduced
2. Markov chain of 3rd order (planned: hybrid-order Markov chain)
3. using stochastic monthly generator to reproduce intermonthly
variability of means of SRAD, TMAX, TMIN and PREC
Markov chains of higher order
data:
validation:
(details: poster)
17 Czech stations; 1 UK, 5 Switzerland; 17US
3030y synthetic vs 30y observed time series
a) 1st order Markov chain for European stations:
- number of long (L>10d) dry/wet spells: underestimated (autumn, winter)
- max. length of dry/wet spells is underestimated (esp. dry spells in winter)
- Wilcoxon statistics: worst performance for dry spells in winter !!!!
b) higher order Markov chains (parameters for individual seasons):
- improvement, especially for dry spells in winter
- 3rd Markov chain brings only slight improvent with respect to 2nd order
Fig. 6 Number of dry spells (longer than 10 days) winter.
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.10
Monthly weather generator:
variables: ln<SRAD>, <TMAX>, <TMIN>, <PREC>1/4
model:
standardised deviations ~ AR(1) model
linking monthly and daily weather generators:
adjustment of the daily values to monthly series:
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.11
validation of the new version of the generator:
a) effect on stochastic structure of synthetic weather series
- annual cycle of correlations and lag-1 correlations is perfectly reproduced
- reproduction of dry / wet spells is improved (→ Fig. 6)
- variability of monthly / seasonal / annual means is improved (→Fig. 7)
b) effect on crop modelling and hydrological modelling
 CERES-Wheat: variability of wheat yields → Fig. 8
- slight improvement
 SAC-SMA:
a) variability of monthly streamflow characteristics → Fig. 9
- improved reproduction in spring due to monthly generator
b) probability distribution of 5-day average streamflow → Fig. 10
- improved reproduction of extreme streamflows in spring
- due to M(3) model (slight effect)
- monthly generator (stronger effect)
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.12
Fig. 7. Variability of monthly and seasonal means of precipitation
derived from observed (OBS) and synthetic weather series [SYN1 = old
version of WG; AC = annual cycle of AR matrices included; +MC3 = 3rd order
Markov chain used; +MG = monthly generator used].
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.13
Fig. 8 The ratios of the averages (left) and standard deviations (right) of
the 100y model wheat yields simulated with synthetic weather series to
the 30y model wheat yields simulated with observed weather series:
AVG (synt) AVG (model yields simulated with synthetic weather series)

AVG (obs) AVG (model yields simulated with observed weather series)
STD (synt) STD (model yields simulated with synthetic weather series)

STD (obs) STD (model yields simulated with observed weather series)
[SYN1 = old version of WG; +AC = annual cycle of AR matrices included;
+M3 = 3rd order Markov chain used; +MG = monthly generator used]
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.14
Fig. 9 AVGs and STDs of monthly averages (left) and maxima (right) of stramflows simulated by SAC-SMA.
Weather series were generated with various settings of the stochastic weather generator Met&Roll.
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.15
Fig. 10 Probability distribution of 5-day average streamflow [SAC-SMA]
OBS = observed values; CB = simulated with observed weather series
simulated with synthetic weather series generated by:
SYN1 = old version of WG; +AC = annual cycle of AR matrices included;
+MC3 = 3rd order Markov chain used; +MG: monthly generator used]
8th International Meeting on Statistical Climatology *** Lüneburg, Germany *** 12-16 March 2001 *** p.16
Conclusions
previous version of the weather generator:
 discrepancies exist between stochastic structure of observed and
synthetic weather series
 satisfactory results in crop growth modelling
 greater discrepancies in hydrological modelling
improved version of the weather generator:
 annual cycle of AR matrices
 3rd order Markov chain: improves modelling dry/wet spells
 monthly generator:
improves variability of monthly / seasonal / annual means
effect on crop / hydrological modelling:
 annual cycle of AR matrices has insignificant effect
 variability of model wheat yields is slightly improved
 river flow regime simulation is more significantly improved, especially
due to the monthly generator, especially in spring
references:
 Met&Roll (freeware): www.ufa.cas.cz/dub/dub.htm#met&roll
 this presentation: www.ufa.cas.cz/dub/impacts/8imsc.doc
 home page: www.ufa.cas.cz/dub/dub.htm
 Dubrovský, 1997, Environmetrics 8, 409-424. (also on web)
 Dubrovský et al., 2000, Climatic Change 46, 447- 472