GIS in Water Resources (Fall
2008)
Project Report
Statistical Downscaling of GCM Simulations
to Future Temperatures: A Regression-Based Approach
By
Dumindu
Jayasekera
Table of Contents:
- Introduction
- Objectives
- Data
Sources
- Methodology
- Downscaling
using SDSM
- Weather
Station Selection
- Model
Run
- Summary
and Conclusions
- References
1.
Introduction
Global warming became one of the biggest scientific issues during the
1980s. It has continued to attract scientific attention and also political and
public concern. Studies show that earth’s average surface temperature is increasing and this results a change in ocean
temperature, ice and snow cover, and sea level with this global warming (IPCC,
2007). Extensive scientific research
reveals that there is a confidence that human induced greenhouse gas
concentrations are responsible for most of the global warming observed during
the past 50 years.
Since pre-industrial
times, CO2, the most important greenhouse gas, has increased by 31%
(IPCC, 2001). Water vapor is the other most important greenhouse gas.
Increasing in temperature has a positive feedback effect on water vapor
content. Other gases present in the atmosphere in small amounts also contribute
to the greenhouse effect. Collectively, this increase in greenhouse gases has
altered the radiative balance of the earth to the point that it is now having a
distinct influence on the global climate (IPCC, 1996).
2.
Objectives
- Estimate the average minimum temperatures at the
end of this century (2059-2099) by downscaling the large scale simulated
predictor variables from the global models.
- Develop average minimum temperature maps for all
seasons at the end of the century across
3.
Data Sources
- Statistical Downscaling Model (SDSM) predictors
by data portal maintained by the Canadian Climate Impacts Scenarios Group.
(http://www.cics.uvic.ca/scenarios/sdsm/select.cgi)
(http://climate.usurf.usu.edu/products/data.php)
(http://gis.utah.gov)
4.
Methodology
4.1 General Circulation Models (GCMs)
To quantify the
impacts of climate change on temperature, the outcomes of general circulation
models (GCMs) which are known as one of the credible scientific techniques to
simulate the impacts of increased greenhouse gases on climatic variables was
used. But these models are restricted in their usefulness for many subgrid
scale applications by their coarse resolution. Because, regional scale
processes are occurring on spatial scales much smaller than those resolved in
GCMs. Therefore, a technique is needed to relate the atmospheric processes
occurring over a large scale to regional or smaller-scale processes. Bridging
the gap between the resolution of climate models and regional and local scale
processes represents a considerable problem for the impact assessment of
climate change, including the application of climate change scenarios to
hydrological models. Thus, considerable effort in the climate community has
focused on the development of techniques to bridge the gap, known as
‘downscaling’.
GCM scenario developed
by HadCM3 (
4.2
Overview of Downscaling Methods
Two fundamental approaches exist for the downscaling
of large-scale GCM output to a finer spatial resolution. First is a dynamical
approach where a higher resolution climate model is embedded within a GCM.
Second is to use statistical methods to establish empirical relationships
between GCM-resolution climate variables and local climate. These two
approaches are described below and the main advantages and limitations of each
are summarized in Table 1.
Table 1. Comparison of advantages and
disadvantages of statistical and dynamical downscaling techniques (Adapted from
Wilby and Wigley, 1997).
|
|
Statistical Downscaling |
Dynamical Downscaling |
|
Advantages |
·
Comparatively
cheap and computationally efficient. |
· Produces
responses based on physically consistent process. |
|
|
·
Can provide point-scale climatic variables
from GCM-scale output. |
· Produces
finer resolution information from GCM-scale output that can resolve
atmospheric processes on a smaller scale. |
|
|
·
Can be used to derive variables not
available from Regional Climate Models (RCMs). |
|
|
|
·
Easily transferable to other regions. |
|
|
|
·
Based on standard and accepted statistical
procedures. |
|
|
|
·
Able to directly incorporate observations
into method. |
|
|
Disadvantages |
·
Require long and reliable observed
historical data series for calibration. |
· Computationally intensive. |
|
|
·
Dependent upon choices of predictors. |
· Limited
number of scenario ensembles available. |
|
|
·
Non-stationarity in the predictor-predictand
relationship. |
· Strongly
dependent on GCM boundary forcing. |
|
|
·
Climate system feedbacks not included. |
|
|
|
·
Dependent on GCM boundary forcing; affected
by biases in underlying GCM. |
|
|
|
·
Domain size, climatic region and season affect
downscaling skill. |
|
4.3
Statistical Downscaling
More sophisticated
downscaling methods are generally classified into three groups.
1)
Regression methods
2)
Weather typing
schemes
3)
Weather
generators
Each group covers a range
of methods, all relying on the fundamental concept that regional climates are
largely a function of the large-scale atmospheric state. This relationship may
be expressed as a stochastic and/or deterministic function between large-scale
atmospheric variables (predictors) and local or regional climate variables
(predictands).
4.3.1
Statistical Downscaling Model (SDSM)
Khan et al (2006b)
showed in an uncertainty assessment of statistical downscaling methods indicates
that the SDSM is the most capable of reproducing various statistical
characteristics of observed data in its downscaled results with 95% confidence
level. This study compared the variances of observed downscaled daily minimum
temperatures at each month of the year, the SDSM model errors were
insignificant in all months of the year at 95% confidence level. In confidence
interval comparison of variances of daily minimum temperatures in each month,
the SDSM model was able to reproduce observed uncertainty in their downscaled
temperature in almost all months of the year.
Therefore, this study uses SDSM model for daily minimum temperature
downscaling.
The Statistical
Downscaling Model (SDSM) empirical-statistical downscaling (ESD) tool is
developed by Rob Wilby and Chris Dawson in
SDSM has
been used extensively for impact studies and is a user-friendly software
package designed to implement statistical downscaling methods to produce
high-resolution climate model. Recent studies based on SDSM are Wilby and Harris
(2006), Khan et al., (2006a), Harpham and
Wilby (2005), Scibek and Allen (2006), Wetterhall, et al., (2007), and Khan et al., (2006b).
4.4
Data Collection
Daily minimum
temperatures (Tmin) from
5.
Downscaling using SDSM
In this study, the
‘observed’ large scale atmospheric predictors from the National Centers for
Environmental Prediction (NCEP) reanalysis data sets were used for calibration
and validation of the downscaling models, and then the derived predictors of
the HadCM3 (Hadley Center for Climate and Prediction and Research, UK) were
used in simulating average monthly minimum temperature for the current period
(1961-2001) and future (2059-2099).
5.1
Overview
of SDSM structure
The SDSM software statistically downscales daily weather
series in seven discrete steps. The steps are,
1) Quality control and data transformation
2) Screening of predictor variables
3) Model calibration
4) Weather generation (using observed predictors)
5) Statistical analyses
6) Graphing model output
7) Scenario generation (using climate
model predictors).
Figure 1. SDSM Version 4.2 climate
scenario generation (Adapted from SDSM 4.2 user manual).
Within the classification of downscaling
techniques, SDSM is best described as a hybrid of the stochastic weather
generator and transfer function methods. This is because large–scale
circulation patterns and atmospheric variables are used to condition
local–scale weather generator parameters. Additionally, stochastic techniques
are used to artificially inflate the variance of the downscaled daily time
series to better accord with observations.
5.2
Main
functions of SDSM
5.2.1 Quality control and data transformation
There can be few
meteorological stations have 100% complete or fully accurate data sets.
Handling of missing and imperfect data is necessary for most practical situations.
The ‘Quality Control’ identifies gross data errors, specification of missing
data codes and outliers prior to model calibration. Transformation function
will apply selected transformations for selected data files.
5.2.2 Screening
of downscaling predictor variables
Identifying empirical
relationships between gridded predictors (such as mean sea level pressure) and single
site predictand (such as minimum temperatures) is vital to all statistical
downscaling methods.
The main purpose of the
screen variables operation is assisting to decide and select appropriate
downscaling predictor variables.
5.2.3 Model
Calibration
This operation takes
user-specified predictand along with a set of predictor variables, and estimates
the parameters of multiple regression equations via an optimization algorithm
by either dual simplex or ordinary least squares methods.
It is needed to specify the
model structure: whether monthly, seasonal or annual sub-models are required;
whether the process is unconditional or conditional. In unconditional models a
direct link is assumed between the predictors and predictand. In conditional
models, there is an intermediate process between regional forcing and local
weather.
5.2.4 Weather
Generator
This operation generates
ensembles of synthetic daily weather series given observed (or NCEP
re-analysis) atmospheric predictor variables. This procedure enables the
verification of calibrated models (using independent data) and synthesis of
artificial time series for present climate conditions.
Also, specification of the
period of record to be synthesized and the desired number of ensembles are needed.
5.2.5 Data
Analysis
This provides means of
interrogating both downscaled scenarios and observed climate data with summary
statistics and frequency analysis. This will allow use r to specify the
sub-period, output file name and chosen statistics. For model output, ensemble
member or mean must also be specified.
5.2.6 Graphical
Analysis
This provides the options
to analyze frequency analysis, compare results and time series analysis.
5.2.7 Scenario
Generation
This operation produces
ensembles of synthetic daily weather variables given atmospheric predictor
variables supplied by a climate model (either for present or future climate experiments),
rather than observed predictors.
6.
Weather Station Selection
The grid size of HadCM3 is
2.5° latitude and 3.75° longitude. There are 3 grid locations over
Length along the meridian:
Length along the parallel:
The maximum grid distance was
319.37 km was along the parallel. The weather stations in a grid location were
selected using the ArcGIS select by location feature. The weather stations were
selected within a distance of 159.68 km which is half of the maximum distance
calculated in the grid by applying a buffer to the feature of the a particular
HadCM3 grid location.
Figure 2. Selection of weather stations of a HadCM3 grid location.
7.
Model Run
Daily minimum temperature
data available from
7.1 Quality
Control
Daily minimum temperature
data was checked for missing values. Any missing data value was coded as -999 and
saved with .DAT file extension.
Figure 3. Quality control check for
7.2 Screen
Variables
Screening variables were
based on the variance explained, partial correlation, and scatter plots between
predictor variable and predictand (Tmin). Assuming that there is a
direct link between predictors and
Figure 4. Screening gridded predictor
variables.
Figure 5. Variance explained by
predictor variables.
Figure 6. Partial correlation of
predictor variables with predictand.
Figure 7. Predictors have linear
relationship with the predictand.
7.3 Model
Calibration
The 6 predictor variables
selected in the above section were used to calibrate the model with the
observed daily minimum temperatures (TMINLoganUSU61_81) for the period from
Figure 8. Model calibration with
observed daily minimum temperatures for 21 years of historical data.
Figure 9. RSquared values of monthly
models and their standard errors.
Figure 10. Residuals plotted against
predicted values.
Figure 11. Histogram of residuals.
7.4 Weather
Generator
The weather generator operation was used to generate
ensembles of synthetic daily weather series for the period from
Figure 12. Weather generation for the
period from 1982_2001.
7.4.1 Model
Validation
The simulated ensembles of
synthetic daily weather series from
Figure 13. Model validation using
average monthly minimum temperatures.
Table 2. Comparison of simulated and
observed mean values.
|
1982-2001 |
OBSERVED |
SIMULATED |
|
|
Month |
Mean |
Mean |
(Error)2 |
|
January |
-9.0480 |
-8.5942 |
0.2059 |
|
February |
-6.3497 |
-6.5753 |
0.0509 |
|
March |
-2.9124 |
-1.7340 |
1.3886 |
|
April |
1.7106 |
2.2526 |
0.2939 |
|
May |
6.5814 |
6.7715 |
0.0362 |
|
June |
10.7753 |
10.7691 |
0.0000 |
|
July |
15.0771 |
14.6664 |
0.1687 |
|
August |
14.1256 |
14.7388 |
0.3760 |
|
September |
8.9221 |
9.2363 |
0.0987 |
|
October |
3.5548 |
2.9890 |
0.3201 |
|
November |
-1.9503 |
-2.5214 |
0.3261 |
|
December |
-7.4477 |
-8.2891 |
0.7081 |
|
|
|
SUM |
3.9732 |
|
|
|
MSE |
0.3311 |
|
|
|
RMSE |
0.5754 |
Figure 14. Plot of simulated mean
versus observed mean.
7.5 Data
Analysis
Figure 15 shows the
quantile-quantile plot plotted using the observed daily minimum temperatures
against the ensemble mean downscaled from HadCM3 for the period from
Figure 15. Quantile-Quantile plot of
observed daily minimum temperatures at LoganUSU
versus the ensemble mean downscaled from HadCM3 for the period 1961_2001.
Figure 16 shows the
probability density function (PDF) of simulated and observed mean values. A
simple empirical distribution was used to obtain the frequency analysis with
95% confidence level (Figure 17).
Figure 16. Probability Density Function
(PDF) of generated using 20 categories.
Figure 17. Frequency analysis using
SDSM.
Figure 18 shows the time series analysis for the simulated
and observed minimum temperatures for the period from
Figure 18. Time series plot of minimum
daily temperature at
7.6 Scenario
Generation
Scenario generation
operation was used to generate the ensembles of synthetic daily weather series
using HadCM3 atmospheric predictor variables for the period from 2059 to 2099
(Figure 19). Summary statistics were calculated for the future climate forcing
(FCF) using the ensembles for the period from 2059 to 2099. The summary
statistics calculated for current climate forcing (CCF) (1961-2001) was
calculated using summary statistics operation and compared with FCF. The
summary statistics for the CCF is shown in Table 3 and Table 4 shows the
summary statistics for the FCF. Comparison of averages of CCF and FCF are shown
in Figure 21.
Figure 19. Scenario generation for
future climate forcing using HadCM3 model.
Figure 20. Summary statistics calculation for FCF.
Table 3. Summary statistics of
observed minimum temperatures (CCF) from 1961-2001.
Table 4. Summary statistics of
simulated minimum temperatures (FCF) from 2059-2099.
Figure 21. Comparison of average
minimum temperatures for CCF and FCF.
7.7 Depiction
of Average Minimum Temperatures across
ArcGIS spline interpolation
function available in spatial analyst tool was used to create average minimum
temperature maps for CCF (1961-2001) and FCF (2059-2099) during winter, spring,
summer and fall. Summary of seasonal temperature values during CCF and FCF are
presented in Table 5.
Table 5. Comparison of seasonal
average minimum temperatures in the past and in the future.
|
|
Winter |
Spring |
Summer |
Fall |
Annual |
|
Celsius (C) |
|||||
|
1961_2001 |
-7.629 |
2.335 |
13.537 |
3.619 |
3.033 |
|
2059_2099 |
-7.509 |
1.825 |
14.718 |
3.157 |
3.048 |
Figure 22. Past and future average
minimum temperatures in Winter across
Figure 23. Past and future average
minimum temperatures in Spring across
Figure 24. Past and future average
minimum temperatures in Summer across
Figure 25. Past and future average
minimum temperatures in Fall across
8.
Summary and Conclusions
- Average annual minimum temperatures will be
increased at the end of this century (2059_2099) if there is no
intervention to mitigate the rate of emission of greenhouse gas emissions.
- Summers will be significantly warmer across
- At the end of this century, southern part of
- On average, winter seasons average minimum
temperatures will increase. Spring and Fall seasons average minimum
temperatures will be decreased in
9.
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