climate data for the australian water availability...
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Climate Data for the Australian Water Availability Project
Australian Water Availability Project
Final Milestone Report
David A. Jones, William Wang and Robert Fawcett
National Climate Centre
Australian Bureau of Meteorology
October 2007
Corresponding author:
Dr David Jones, National Climate Centre, Australian Bureau of Meteorology
GPO Box 1289 Melbourne, Australia 3001. [email protected]
1
Climate Data for The Australian Water Availability Project
Table of Contents
1. Introduction ...............................................................................................................3 2. The Meteorological (in situ) Data ............................................................................3 3. The Spatial Analysis Methodologies........................................................................6 4. Quality of the Analyses...........................................................................................16 5. Near-Surface Wind Run.........................................................................................27 6. Summary and Conclusions.....................................................................................29 7. References................................................................................................................31 Appendix: Climatological Maps for 1971-2000........................................................33
The Australian Water Availability Project (AWAP) is a partnership between the Bureau of Rural Science, CSIRO (EOC and Land and Water), and the Bureau of Meteorology. The overall objective and outcome statement for AWAP are described in AWAP Work Plan 2004-2006, Version 6, 27 September 2004.
2
Summary
The Bureau of Meteorology has generated a range of improved meteorological analyses and
remotely sensed datasets for Australia as a contribution to the Australian Water Availability
Project. The meteorological data include analyses of rainfall, temperature, vapour pressure
and wind run at daily and monthly timescales.
Robust topography-resolving analysis methods have been developed and applied to in situ
observations of rainfall, temperature and vapour pressure to produce analyses at a resolution
of 0.05º×0.05º (approximately 5 km × 5 km) for the period 1980 to the present. The resulting
analyses represent substantial improvements on operational analyses currently produced by
the Bureau of Meteorology. Coarser-resolution analyses of wind run have also been
developed.
This report provides a detailed overview of the project outputs and the analysis systems which
have been used to generate them. Careful attention has been paid to developing systems and
datasets which are robust and useful for the monitoring of both climate variability and climate
change. These systems are now running in real-time and are expected to form the basis for
ongoing monitoring of Australia’s surface climate by the Australian Bureau of Meteorology.
3
1. Introduction
The past year has seen much of Australia suffer from severe meteorological and hydrological
drought. This has seen water resources fall to record lows and agricultural production
massively decline in many regions (e.g., MDBC 2007). There has never been a greater need
for up-to-date information about the state of Australia’s climate and water resources to ensure
that water resources are used in a sustainable manner.
A key to the better management of water is ensuring that demand does not exceed the long-
term supply. At the present time Australia does not have a comprehensive or consistent source
of information on water balance, covering the relationships between rainfall, evaporation,
evapotranspiration, run-off and drainage to surface and ground water. The National Heritage
Trust supported Australian Water Availability Project was designed to address this knowledge
gap. The objective of this project being “to develop an operational prototype of a new and
integrated approach to monitoring and predicting soil moisture and other components of the
water balance” .
An important aspect of this project is the integration of in situ (conventional) meteorological
observations with remotely sensed data, thereby allowing the description of water and climate
at finer space and time scales. The conventional data are temporally dense (Automatic
Weather Stations - AWS - routinely record one minute data) but spatially sparse. In contrast,
the remotely sensed satellite data are often sampled on scales of a few kilometres or finer, but
infrequent, with consecutive views hours or days apart (that is, spatially dense but temporally
sparse).
The Bureau of Meteorology has developed improved spatial analyses to support the
Australian Water Availability real-time hydrological analysis system for Australia. The
meteorological analyses cover precipitation, maximum and minimum temperatures, vapour
pressure and near-surface wind run (Jones et al. 2006). The meteorological analyses (both
daily and monthly averages) are augmented by a series of new remotely sensed data including
global solar radiation from geostationary satellites and Normalised Difference Vegetation
Index (NDVI) and land surface temperature from the Advanced Very High Resolution
Radiometer (AVHRR) on polar orbiting satellites. The remotely sensed data are described in a
separate report.
4
The Meteorological (in situ) Data
The data and analyses described in this report are largely based on conventional
meteorological observations from weather stations (“Meteorological Data”). New spatial
analysis techniques have been used to generate high-resolution surfaces from these
observations. The methods employed are described in this report.
Variable
Source
Temporal Resolution
Spatial Resolution
Precipitation Analysis of rain gauge data
Daily and monthly average
0.05°×0.05°
Daily Maximum Temperature
Analysis of thermometer data
Daily and monthly average
0.05°×0.05°
Daily Minimum Temperature
Analysis of thermometer data
Daily and monthly average
0.05°×0.05°
Vapour Pressure “Humidity”
Analysis of dewpoint data
Daily and monthly average of 9am and 3pm
0.05°×0.05°
Near Surface Wind Run
NCEP/NCAR numerical model analysis
MesoLAPS numerical model analysis
Daily and monthly average
Daily and monthly average
2.5°×2.5°
0.042°×0.042°
Table 1: Description of the meteorological data.
The meteorological variables and analyses are summarised in Table 1. Maximum and
minimum temperature, rainfall and vapour pressure fields (from dewpoint) have been
generated through the geostatistical analysis of observations at weather stations (a mix of
manual and AWS observations). The analyses are derived from daily and monthly data
contained in the Australian Bureau of Meteorology climate databank (Australian Data
Archive for Meteorology - ADAM). ADAM is updated in real-time, thereby allowing
analyses of new data to be produced in a timely fashion. Over the analysis period (1980 to
2006) the rainfall network contains an average of 5760 stations, while there is an average of
721 temperature stations and 670 dew point (“vapour pressure”) stations (see Figure 1). The
near-surface wind run analyses come from a numerical weather model-based assimilation
scheme as described below.
5
(a)
(b)
(c)
Figure 1: The networks of (a) rainfall, (b) temperature and (c) dewpoint temperature (“vapour
pressure”) stations contributing to the analyses from 1980 to 2006.
6
For rainfall, the daily data represent the precipitation (including rain, snow, hail and dew)
accumulated in the 24 hour period to 9am. The maximum and minimum temperatures are the
highest and lowest temperature for the 24-hour period starting/ending 9am, respectively. This
convention means that the minimum and maximum temperatures will have generally occurred
on the same calendar day (in the morning and afternoon, respectably). The vapour pressure is
that observed at 9am and 3pm local time. These two times have the best data coverage for
Australia. We note that the vapour pressure has a rather weak diurnal cycle through the day
(Jeffrey et al. 2001, Appendix). The vapour pressure has been calculated at stations using
observations of dewpoint temperature following Murray (1967).
It is not possible to sensibly analyse wind from surface anemometer observations alone. This
is because wind is particularly sensitive to local factors such as station location and exposure.
This sensitivity leads to large errors of representativeness with individual observations being a
poor indicator of the overall field of wind (Daley 1993). The nature of this problem varies
with the landscape. For example, mountainous areas will have complex wind patterns where
individual wind observations may be quite misleading, whereas flat farming areas will tend to
be less complex and individual wind observations may be broadly representative.
The near-surface wind field is related to the air temperature and pressure (Holton 1992). For
this reason representative wind analyses can be created using a multivariate analysis approach,
such as is used for numerical weather prediction (NWP). In this project we have generated
wind products from two sources. A long historical sequence back to 1980 has been generated
from the National Centers for Environmental Prediction (NCEP)/National Center for
Atmospheric Research (NCAR) reanalyses (Kalnay et al. 1996) described below. These
coarse resolution data have been augmented with very high resolution Bureau wind analyses
at approximately 4 km resolution for the period from 2005 to the present. These analyses are
based on the Bureau’s regional weather forecast model MesoLAPS (Puri et al., 1998) as
described below.
2. The Spatial Analysis Methodologies
The maximum temperature, minimum temperature, vapour pressure and rainfall fields are
based on the spatial analysis of meteorological observations. The observations are from the
Bureau of Meteorology’s ADAM climate database. The underlying station networks have
generally improved slightly over the period of analysis (Figure 2), meaning that the
underlying analyses should improve with time.
7
Generating daily analyses of meteorological data which are consistent with monthly and long-
term analyses is not straight-forward (Rayner et al. 2004). Temporal averaging dampens the
small scale variability while random observational errors are also reduced by time averaging.
In addition, the relationship with topography is more robust on longer time scales. This means
that the monthly average fields are smoother and observations relatively less error prone. As a
result the monthly average is simpler to analyses than daily data. An added complication is
the fact that some stations have digitised monthly data but not digitised daily data and vice
versa (Jones and Trewin 2002).
It is reasonable to require that the analysis fields
• provide a more accurate representation of short-term climate than does the long-term
average (or climatology);
• be consistent with long-term averages (or climatology); and
• have values which are limited to a physically realistic range.
The last of the points while seemingly trivial is important as it is possible for interpolated
surfaces to become quite unrealistic in data voids when meteorological gradients are strong.
We have developed an anomaly-based approach for analysing rainfall, vapour pressure and
temperature. The new approach is similar to the system described by Hunter and
Meentemeyer (2005) and Xie et al. (2007). It uses a decomposition of the meteorological
variable being analysed into a long-term average component and an anomaly component. The
basis for this decomposition is that anomalies tend to be rather smoother that the raw fields
and that climatology provides information beyond that contained in individual station
observations alone.
The analysis methodology represents an extension of the background/increment method of
analysis which is popular for meteorological (weather and climate) analysis (e.g., Koch et al.
1983; Daley 1992; Jones and Trewin 2000). It is important that systems which are to be used
operationally as part of this project are robust and hence the similarity with these systems is a
positive.
An advantage of the anomaly approach is that anomalies tend to be weakly related to altitude
(owing to the tendency for the atmosphere anomalies to be approximately barotropic) and so
can be adequately analysed with a two-dimensional analysis procedure. In addition the
average of all analyses will, by design, be consistent with the underlying climatology.
8
0
1000
2000
3000
4000
5000
6000
7000
8000
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
Year
Num
ber
of R
eportin
g R
ainfa
ll Sta
tions
(a)
0
200
400
600
800
1000
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
Year
Nu
mb
er o
f R
epo
rtin
g S
tati
on
s
Vapour Pressure
Temperature
(b)
Figure 2: The number of stations contributing to the (a) rainfall and (b)
temperature and vapour pressure analyses by year.
We have used the Barnes successive-correction method for the analysis of the anomalies
(Koch et al. 1983; Seaman 1989; Jones and Weymouth 1997) and three-dimensional
smoothing splines for the analysis of climatological averages (Hutchinson 1995). These two
9
techniques have been used widely in meteorological applications previously and have been
shown be robust (e.g., Hutchinson 1995; Jones and Trewin 2000; BoM 2000). The Barnes
method has a number of advantages including being computationally efficient, robust (coping
with strong gradients and data voids) and tuneable. In some contrast, the spline method is
particularly suited to analysing the rather smooth climatological relationships between
meteorological variables and latitude, longitude and altitude but not well suited to noisy data.
These analysis methods are both “statistically” optimal, in that the analysis fields have the
smallest error subject to the constraints on the final analysis. The analysis methods have been
implemented in a modular fashion, which allows for the use of alternative methods for
generating the climate (background) and anomaly (increment) fields in future.
Application to Temperature and Vapour Pressure
In the following, data values at a station k (k = 1,…,S) are denoted with a suffix k, while
analysis values are defined at locations (x,y,z), the coordinates being latitude, longitude and
altitude. Values are defined at a series of time points, denoted by t (t = 1,…,N). The over-bar
denotes a simple temporal average, taken over a 30-year period, following World
Meteorological Organization convention. We have chosen to use the 1971-2000 period as the
base climatology rather than 1961-1990 to improve data coverage. This representation leads
to
)()( tTTtT ′+= (1)
in general,
)()()( tTtTtT kkk ′+= (2)
at stations, and
),,(),,(),,,( tyxTzyxTtzyxT ′+= (3)
for the analysis as a whole. We note in (1), (2) and (3) that the anomaly may be for a day or a
month, both taken from the monthly climatology (1971-2000).
10
(a)
(b)
11
(c)
Figure 3: Climatological (monthly) average for February (1971-2000) (a), daily
anomaly analysis (b) and summation (c) for maximum temperature on 1st
February 2007. Maps (a) and (b) represent the first and second terms on the
right-hand-side of equation (3).
Application to the period 1971 to 2000 and beyond
The anomaly analysis is calculated using an optimal two-dimensional Barnes successive
correction analysis procedure, as described in Jones and Trewin (2000) analysed to location
(x,y). This leads to
�� =
=
′=′S
kkkS
kk
tTyxWyxW
tyxT1
1
)(),(),(
1),,( . (4)
The weights Wk(x,y) in equation (4) are obtained using the iterative Barnes algorithm
described by Jones and Weymouth (1997). The weights have been found via exhaustive cross-
validation following Seaman (1989).
The climatological (temporal-mean) analysis is calculated using three-dimensional smoothing
splines following Hutchinson (1995);
12
),,(),,( ,...,1zyxFzyxT
STT= . (5)
The subscripts on the spline function F(x,y,z) are intended to indicate that the spline function
is dependent on the climatological station data STT ,...,1 . The combined analysis is a simple
sum of the climatological analysis (5) and the anomaly analysis (4);
)(),(),(
1),,(),,(),,(),,,(
1
1
,...,1tTyxW
yxWzyxFtyxTzyxTtzyxT
S
kkkS
kk
TT S�
� =
=
′+=′+= . (6)
An example of this procedure is shown in Figure 3 for daily temperature. The rainfall,
temperature and vapour pressure climatologies for January and July are shown in the
Appendix.
Incomplete Records
The incomplete climate records at stations introduce difficulties in defining the 30-year mean
(1971-2000) at stations and hence in forming (1), (5) and (6). While some stations will have
30 years of data (or nearly so), many stations have incomplete records. The incomplete
records may, however, provide additional useful information for both the climatology and
anomaly analysis. The use of incomplete station records introduces a trade-off between spatial
sampling and temporal completeness when deriving climate means and anomaly analyses.
Let Nk be the number of observations available at the station for the calendar month under
consideration. For a station with a complete or nearly complete record (Nk � 30), we have
)(1
1
tTN
TkN
tk
kk �
=
= . (7)
Using data for stations with short records requires us to form an estimate of the true 30-year
average. We have achieved this using a trade-off between the station’s temporal average
(using all available observations) and an estimate of the temporal average calculated by
interpolation to the station location of the smoothing spline analysis (5). The spline analysis is
obtained using only stations with complete or near-complete records. We thus have available
two alternative and independent estimates for the station average at station k with Nk < 30;
)(1 30
1
tTN
TkN
tk
kk �
<
=
≈ (8)
and
13
),,(),,()(
1),...,(
1),(
1),...,(
1 30
1
301
11
1
301
11
1
301
11
1
kkktT
NtT
NtT
NtT
N
kkkk zyxFzyxTTSN
tS
S
kN
tk
k
kN
tk
k
N
t����≈
=
≈+
=+
+
≈−
=−
−
≈
=
=≈ . (9)
We have chosen to use a linear combination of these two different estimates, with the weights
chosen through an optimisation process using cross-validation;
���
�
���
�−+�
�
���
�≈
����
<
=≈
=
≈+
=+
+
≈−
=−
−
≈
=
� ),,()1()(1
)(1
),...,(1
),(1
),...,(1
30
1
30
1
301
11
1
301
11
1
301
11
1
kkktT
NtT
NtT
NtT
N
N
tk
kk zyxFwtT
NwT SN
tS
S
kN
tk
k
kN
tk
k
N
t
k
. (10)
Cross-validation showed that for stations with Nk ≥ 12, it is better to use the simple temporal
average (8) of the available observations, while for Nk < 12 it is better to take a weighted
combination of the two estimates (8) and (9). This optimisation also revealed that the final
analysis accuracy is only weakly dependent on the exact form of the weights in (10). Figure 4
shows the optimal linear weights for this sum obtained for the analysis of rainfall (the same
weights have been applied to all fields for consistency). We note that in (5) and (9) the
stations used are thus those with Nk ≥ 12, rather than Nk � 30, consistent with the weights.
Climate Weightings
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
N
Wei
ght
Climate Weight
Spline Weight
Figure 4: Linear weights for deriving the temporal average in (10).
Application to Rainfall
Rainfall differences from climatology contain a substantial topographical signature and are
generally no smoother (and indeed they may even be noisier) than the raw rainfall fields
themselves. In contrast, the rainfall percentage of mean shows rather less topographical
14
signature than simple rainfall anomalies. For rainfall, we have defined the anomalies using
division rather than subtraction. The equivalent equations to (1), (2) and (3) for rainfall are
)()( tRRtR ′×= (11)
in general,
)(tRRR kkk ′×= (12)
at stations and
),,(),,(),,,( tyxRzyxRtzyxR ′×= (13)
for the analysis.
The form of the final analysis comparable to (6) becomes
),,()(),(),(
1),,(),,(),,,( ,...,
1
1
1zyxFtRyxW
yxWzyxRtyxRtzyxR
SRR
S
kkkS
kk
×
����
�
�
����
�
�
′=×′= �� =
=
. (14)
As before, climate averages at stations are calculated using (7) and (10) applied to rainfall.
The rainfall climatology for January and July is shown in the Appendix.
Measuring The Accuracy of the Analysis Process
The accuracy of the spatial analyses has been determined through cross-validation at stations.
Validation results have been calculated for the five years 2001-2005 (see Jones and Trewin
2000). This period has been chosen as it is fully independent of that used to define the
climatology. The 2001 to 2005 period is sufficiently long that it covers a range of climate
regimes and so should be a robust estimate of the analysis accuracies overall. We note that the
climatological analyses are not significantly influenced by individual stations so the impact of
not cross-validating this step is insignificant (though using 2001-2005 avoids this
approximation).
Cross-validation has been achieved by randomly deleting 5% of the stations in the network,
performing an analysis using the remaining 95% of station observations and then calculating
the analysis errors for the omitted stations. This process was repeated 20 times for each
month/day providing independent verification statistics for every station. The errors at
stations have been used to generate maps of analysis error and to generate all-station average
errors. As noted previously the network has not changed significantly since 1980, so this five
15
year period should be representative of the overall analysis accuracy for the 1980 to present
period.
Jones et al. (2006) describe a range of issues with the method of cross-validation. Importantly,
cross-validation will give somewhat inflated analysis errors, as the method involves a
degrading of the data network compared to reality (e.g., Jones and Trewin 2000; Jeffrey et al.
2001).
In addition, calculating analysis errors by independent cross-validation against station
observations introduces a bias due to observation “error” (see Daley 1993; Jones and Trewin
2002). Consider a cross validated estimate of a station value T at station k and time t, denoted
by ),,,(ˆ tzyxT kkk . This is calculated using the 95% of the network which is retained in the
cross-validation step. This is a cross-validated version of (6). The cross-validated analysis
error is given by
)(),,,(ˆ)( tTtzyxTtE kkkkk −= . (15)
Aggregating across time, we can calculate a station Root Mean Square (RMS) analysis Error
(RMSE) at the station
[ ] [ ]��==
−==N
tkkkk
N
tkk tTtzyxT
NtE
NRMSE
1
2
1
2 )(),,,(ˆ1
)(1
. (16)
Note that N will vary from station to station and according to whether the analysis is for daily
or monthly data. The observation Tk(t) can be divided into a “true” component and an
“observational error” component ek(t). The true component is what would be measured if the
observation at station k was completely accurate, while the error component is the error
introduced due to factors such as instrument miscalibration, misreading by the observer,
errors in spatial representativeness arising from specific factors at the observation site and so
on. Hence we have
)()()( tetTtT kTrue
kk += , (17)
giving
( ))()(),,,(ˆ)( tetTtzyxTtE kTrue
kkkkk +−= (18)
and
16
( )[ ]�=
+−=N
tk
Truekkkkk tetTtzyxT
NRMSE
1
2)()(),,,(ˆ
1. (19)
On the assumption that the observational errors are statistically independent of the
interpolated and true values (Daley 1993), this can be further simplified to
( ) [ ] [ ]
( ) ( ) .
)(1
)(),,,(ˆ1
22
1
2
1
22
Obsk
Truek
N
tk
N
t
Truekkkkk
EE
teN
tTtzyxTN
RMSE
+=
+−= ��== (20)
In (20)( )2TruekE is the “true error variance” and is a measure of the accuracy of the analysis
in estimating the true field. This value is the true analysis error. The second term ( )2ObskE is
the “observational error variance” and measures the accuracy of the observations. Clearly,
even a perfect analysis will have a non-zero cross-validated error because observations
have some level of error. To obtain a zero cross-validated error, the observations need to be
“perfect”. While it is common practice for the cross-validated differences between
independent observations and analyses to be treated as “analysis errors”, and they are
defined as such here, it is important to keep in mind that they also contain an observation
error component. Daley (1993) and Jones and Trewin (2000) describe how the
observational errors can be estimated.
In defining the analysis errors averaged across time and stations we have used the
additional measures of bias and Mean Absolute Error (MAE). These are both defined in
the usual way (e.g., Jones and Weymouth 1997),
[ ]�=
=N
tkk tE
NBIAS
1
)(1
(21)
and
�=
=N
tkk tE
NMAE
1
)(1
(22)
The all station average is these terms extended across stations,
[ ]� �= =
��
���
�=
S
k
N
tk
k
k
tENS
BIAS1 1
)(11
(23)
17
and
� �= =
��
���
�=
S
k
N
tk
k
k
tENS
BIAS1 1
)(11
. (24)
3. Quality of the Analyses
Cross-validated analysis statistics for the five years 2001 to 2005 are provided in Tables 2 to 4,
with maps of RMSE in Figures 6 to 8. For reference, we also provide national average
statistics for the operational Barnes analysis system used at the Bureau of Meteorology (see
Jones and Weymouth 1997; Jones and Trewin 2000). There are no operational analyses for
vapour pressure, so a comparison is not possible for this variable. We note that these
verification results are not exactly comparable to those provided by Jones and Weymouth
(1997) and Jeffrey et al. (2001), because of slightly different cross-validation procedures and
different verification periods.
The RMSE for monthly maximum and minimum temperatures are typically between 0.5 and
1ºC, while those for daily temperatures are a little larger at around 1 to 2ºC. There is a strong
correspondence between station density (Figure 1) and analysis error (Figures 5 and 6), with
larger errors occurring through the poorly observed western interior.
The new analyses are a substantial improvement on current Bureau practice for maximum and
minimum temperatures at both the monthly and daily time scales. For maximum temperatures,
the RMSE is reduced by around 40% for daily and nearly 60% for monthly analyses. The
percentage improvement for minimum temperatures is about half as much, but still substantial
at around 0.5ºC for RMSE.
Mean (ºC) Bias (ºC) RMSE (ºC) MAE (ºC) Monthly Maximum Temperature AWA 24.8 0.00 0.7 0.5 Operational 24.8 0.02 1.6 1.1 Monthly Minimum Temperature AWA 12.7 0.00 1.0 0.7 Operational 12.7 0.00 1.5 1.1
(a)
18
Mean (ºC) Bias (ºC) RMSE (ºC) MAE (ºC) Daily Maximum Temperature AWA 24.8 0.02 1.2 0.9 Operational 24.8 0.00 1.9 1.3 Daily Minimum Temperature AWA 12.7 −0.05 1.7 1.3 Operational 12.7 0.03 2.1 1.5
(b)
Table 2: Verification statistics for the five-year period 2001 to 2005. Monthly
maximum and minimum temperatures (a) and daily maximum and minimum
temperatures (b).
The improvement in the temperature analyses is quite general across Australia. The most
substantial improvements are in regions of significant topography. For example, near the
Victorian Alps and Snowy Mountains the RMSE is reduced from more than 2ºC to around
0.6ºC for daily data (not shown). Similar improvements have been reported by Hunter and
Meentemeyer (2005) for California.
The spatial maps of analysis error for maximum and minimum temperatures (Figures 5 and 6)
show little evidence of increased values near significant topography. This confirms that the
anomalies at both timescales tend to be approximately barotropic. These results support the
two-step approach with the use of a two-dimensional anomaly analysis.
Spatially the RMSE highlights regions where spatial analysis is particularly difficult or the
network insufficiently dense. There is some evidence that analysis errors for maximum
temperature are larger near the coast around northwest Australia and about the Nullarbor Plain,
with the areas near Shark Bay and Eucla standing out in particular. These two coastal regions
often experience very strong gradients in maximum temperatures between the inland deserts
and coasts, and are difficult to analyse with a relatively sparse network. It is possible that
much of the coast of Western Australia and parts of the Northern Territory experience similar
issues during the warmer period of the year.
19
(a)
(b)
Figure 5: Cross-validated RMSE for monthly maximum (a) and minimum (b)
temperatures. The units are ºC.
Analysis errors for minimum temperature are greater than those for maximum temperatures.
This is because minimum temperatures tend to have larger errors of representativeness and
shorter length scales (see Jones and Trewin 2000). In addition minimum temperatures often
show complex and variable relationships with topography (e.g., Trewin 2005). These factors
mean that a denser network is required for minimum temperature to achieve the same analysis
20
accuracy as that for maximum temperature. This will be clearly important for analysing
events such as frosts where a difference of 1 to 2ºC may be very significant. We note that the
RMSE for monthly maximum and minimum temperatures are now not much larger than the
theoretical lower bounds calculated by Jones and Trewin (2000, 2002) in parts of inland
eastern Australia. This suggests that in these regions future analysis improvements will
require the use of quite different analysis procedures and new datasets, such as those obtained
by remote sensing.
(a)
(b)
21
Figure 6: Cross-validated RMSE for daily maximum (a) and minimum (b)
temperatures. The units are ºC.
The monthly rainfall analyses show a modest but significant improvement over current
Bureau practice, and are about half those reported previously for Australian analyses (Jeffrey
et al. 2001). The analysis improvement is most marked in southern Australia where the
climatological signals encapsulated in the climate means are more robust. We note that the
RMSE is substantially larger than the MAE. This is because of a significant skewness in the
distribution of rainfall errors, with a relatively small number of large errors.
There is a marked north-south gradient in the RMSE for rainfall across Australia (Figure 7).
In part this reflects the higher rainfall in the tropical regions which will lead to larger analysis
errors for a given data smoothness and network (see Daley 1993). This pattern has been noted
previously by Mills et al. (1997), Jones and Weymouth (1997), and Jeffrey et al. (2001). This
pattern is further amplified by the tendency for rainfall to be highly convective in tropical
parts and hence to have shorter characteristic length scales (e.g., Mills et al. 1997; Ebert et al.
2007).
Mean (mm)
Bias (mm)
RMSE (mm)
MAE (mm)
MAE/Mean (%)
Monthly Rainfall AWA 53.7 0.2 20.8 11.3 21 Operational 53.7 0.1 23.7 12.6 23
(a)
Mean (mm)
Bias (mm)
RMSE (mm)
MAE (mm)
MAE/Mean (%)
Daily Rainfall AWA 1.9 0.0 3.7 1.1 57 Operational 1.9 0.0 3.8 1.1 57
(b)
Table 3: Verification statistics for the 5 year period 2001 to 2005. Monthly
rainfall (a) and daily rainfall (b).
The RMSEs for daily rainfall are very similar to those for the Bureau’s current operational
system and those reported elsewhere for Australia (Mills et al. 1997; Jeffrey et al. 2001). The
insensitivity of the errors to the analysis method is somewhat surprising, given that the
underlying analysis systems are different. To some extent, these findings may be interpreted
by the observation that for daily rainfall the relationship with topography is not particularly
22
strong or robust, so the advantage of using topography is not great (though clearly on
individual days and cases this may not be true). This link to topography is particularly weak
in northern Australia where rainfall is more convective.
(a)
(b)
Figure 7: Cross validated RMSE for monthly (a) and daily (b) rainfall. The units
are mm.
Hunter and Meentemeyer (2005) found rather little positive impact from including climate-
topography relationships in daily rainfall analyses in California. A possible way of improving
23
the analyses might be to develop rainfall-altitude relationships (climatologies) which are
conditional on weather type such as light wind convective situations versus strong on-slope
flow situations.
We also note that the analysis errors for daily rainfall are only weakly dependent on the
Barnes parameters obtained through the optimisation process described by Seaman (1989).
Mills et al. (1997); Weymouth et al. (1999) and Jeffrey et al. (2001) found similar
insensitivities in their analyses of daily rainfall. We interpret this as indicating that the length
scales for rainfall vary markedly from day to day (and also spatially), and hence are not well
approximated by a single parameter set. It is clear that substantial improvements in daily
rainfall analyses will require either far denser networks, or the use of remotely sensed and/or
model-derived data (e.g., Ebert et al. 2007).
Mean (hPa)
Bias (hPa)
RMSE (hPa)
MAE (hPa)
Monthly Vapour Pressure AWA 9am 13.7 0.03 1.1 0.7 AWA 3pm 13.1 −0.05 1.5 1.1
(a)
Mean (hPa)
Bias (hPa)
RMSE (hPa)
MAE (hPa)
Daily Vapour Pressure AWA 9am 13.7 0.02 1.8 1.2 AWA 3pm 13.1 −0.06 2.4 1.6
(b)
Table 4: Verification statistics for the 5 year period 2001 to 2005. Monthly
vapour pressure (a) and daily vapour pressure (b).
Figure 8 shows the distribution of analysis errors for monthly and daily vapour pressure (at
9am). The errors for 3pm are similar (see Table 4) though they tend to be a little larger,
particularly in the north. Following the climatological field (Appendix), vapour pressure
analysis errors increase towards the north where the background means are substantially
higher. There is also evidence of somewhat increased errors close to the coast, where
gradients often tend to be large between moist maritime air and drier continental air, in
agreement with Jeffrey et al. (2001). The lowest analysis errors are found in the well sampled
southeast and southwest parts of Australia.
24
These vapour pressure analyses are the first of their type to be produced by the Bureau of
Meteorology, and consequently they cannot be directly compared to existing analyses.
Comparison with Jeffrey et al. (2001) suggests these analyses may be a little better. An
important observation is the absence of inflated errors near topography. This suggests that the
vapour pressure/altitude relationship is rather robust and amenable to the two-step anomaly
analysis method we have developed.
(a)
(b)
25
Figure 8: Cross-validated RMSE for monthly (a) and daily (b) 9am vapour
pressure. The units are hPa.
Some Case Examples
The analysis statistics reveal that the analyses developed through this project are a substantial
improvement (with the exception of daily rainfall). Importantly, these improvements are
evident in most individual analyses. In this section we consider in some detail two recent
examples for monthly and accumulate daily rainfall.
Figure 9 shows the monthly rainfall for June 2004 across Tasmania using the new anomaly
approach, the operational Bureau analysis and from raw station observations. Nationwide, the
monthly analyses have a MAE of 7.9 mm (for the AWA analysis) and 10.3 mm (for the
Barnes operational analysis), revealing a substantial overall improvement. For Tasmania the
MAE values are 20.7 mm and 30.0 mm, respectively, revealing a large improvement in the
accuracy of the rainfall analysis. These can be compared to the Tasmanian station mean for
June 2004 of 151 mm.
Clearly, there is a marked improvement in the representation of Tasmanian rainfall in Figure
9c. The high rainfall in the west, central highlands and northeast are all well captured as is the
tight rainfall gradients in the central parts of Tasmania. To the east the low rainfall about the
coast and near Hobart is also well captured.
(a)
(b)
26
(c)
Figure 9: Monthly rainfall for June 2004. The current operational analysis (a),
observed totals (b) and AWA analysis (c). The units are mm.
A second example is for the three week period 1st to 21st of June 2007. This period witnessed
severe flooding on the New South Wales coast following a sequence of three major low-
pressure systems. The new analyses show a substantial improvement in the resolution of the
very high rainfall on the coast near Newcastle and secondary maxima south of Sydney and
near the Blue Mountains.
27
(a)
(b)
(c)
Figure 10: Rainfall for the 1st to 21st of June 2007. The current operational
analysis (a), observed totals (b) and AWA analysis (c). The units are mm.
4. Near-Surface Wind Run
The primary wind-run data developed for the project are compiled from 6-hourly (near
surface) 0.995 sigma level winds extracted from the NCEP/NCAR reanalyses (Kalnay et al.
1996). The 0.995 sigma level is about 40 metres above the surface. These wind analyses are
based on a numerical weather prediction model-based analysis system incorporating global in
28
situ and remotely sensed data. Given their global extent, these data are on a coarse 2.5°×2.5°
grid (which in the Australian region represents approximately a 250 km×250 km grid). The
analysed wind field is restricted to capturing synoptic-scale wind patterns, with local affects
such as down-slope winds and some sea breezes likely to be missed. It is not possible to
generate sensible analyses for wind using conventional univariate analysis techniques due to
large errors of representativeness at wind observation sites (e.g., Rayner et al. 2004) and a
network which is insufficiently dense for the purpose.
The development of improved wind mapping for Australia is an area of ongoing
research at the Bureau and elsewhere. A gridded hourly analysis of 10-metre wind with
a grid resolution of approximately 4 km×4 km is presently being trialled in the Bureau,
based on short range meso-scale weather forecasts modified with real-time wind
observations. Miller and Benjamin (1992) describe the application of a similar system in
the United States.
Daily and monthly wind run fields are being derived from this system by calculating the wind
speed (the magnitude of the wind vector) at each analysis hour for each grid point and taking
that to be the average wind speed for the entire hour. An appropriate scaling, summed over
the 24 analyses, gives the daily wind run. It is then aggregated to provide a monthly wind run
(expressed for convenience in units of km/day). Data for this new system are only available
from late 2004 onward. Examples of the very high resolution daily and monthly wind run
calculations are shown in Figures 11 and 12 respectively.
Figure 11: A very high resolution wind run analysis for 31 May 2007. The units
are km/day.
29
Figure 12: A very high resolution wind run analysis for May 2007. The units are
km/day.
6. Summary and Conclusions
In this report we have provided a detailed description of a series of new meteorological
analysis products developed by the Australian Bureau of Meteorology as a contribution to the
Australian Water Availability Project. Careful attention has been paid to developing systems
and datasets which are robust and useful for the monitoring of both climate variability and
climate change. These systems are now running in real-time and are expected to form the
basis for ongoing monitoring and mapping of Australia’s climate by the Australian Bureau of
Meteorology.
The analyses make use of a new two-step analysis system which partitions the analysis field
into a climatological component and an anomaly component. This approach has been found to
be robust, to preserve the background climatology in the long-term and to be computationally
efficient. These systems are seen as a substantial improvement on existing Bureau practice
and are comparable with international practice.
There are ongoing issues which have emerged through this study and which will be the focus
of future development and work. Foremost, there is a need to improve the daily rainfall
analyses, for which all currently available Australian analyses have less than impressive
accuracies. The evidence is that this will require either very different analysis techniques
which make use of data not currently used (such as from remote sensing and numerical
weather prediction) or a substantial improvement in the national rain-gauge network.
30
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data for climate monitoring. Australian Meteorological Magazine, 51, 237-250.
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Jones D.A., Wang W., Fawcett R. and Grant I. 2006. The generation and delivery of Level-1
historical climate data sets. Australian Water Availability Project Milestone Report. 32pp.
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Report No. 70, Bureau of Meteorology, Melbourne, Australia. 19pp.
Kalnay E., Kanamitsu M., Kistler R., Collins W., Deaven D., Gandin L., Iredell M., Saha S.,
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Appendix: Climatological Maps for 1971-2000
(a)
(b)
Figure A1: The monthly average maximum temperature for January (a) and July (b). The units are ºC.
33
(a)
(b)
Figure A2: The monthly average minimum temperature for January (a) and July (b). The units are ºC.
34
(a)
(b)
Figure A3: The monthly average 9am surface vapour pressure for January (a) and July (b). The units are hPa.
35
(a)
(b)
Figure A4: The monthly average 3pm surface vapour pressure for January (a) and July (b). The units are hPa.
36
(a)
(b)
Figure A5: The monthly average rainfall for January (a) and July (b). The units are mm.