Final Draft Report To

MOE Grant Project: Developing High‐Resolu on 

(45km x 45km) Probabilis c Climate Projec ons 

Over Ontario from Mul ple Global and Regional 

Climate Models 

Submi ed by the LAMPS Team 

Contact: 

Dr, Xin Qiu and Huaiping Zhu 

LAboratory of Mathema cal Parallel Systems  

Ross Building N532 York University 

Phone: 416‐7362100, Ext: 20188 

Fax: 416‐7365757 

Email: huaiping@mathstat.yorku.ca 

March 26, 2012 

Executive Summary The MOE probabilistic climate change downscaling project was completed by two main tasks: 1)

High Resolution Climate Change Scenario on Annual HDD and CDD; 2) High Resolution

Climate Change Scenario on Precipitation. For Task 1, “High Resolution Climate Change

Scenario on Annual HDD and CDD”, as an extension of the work of Li et al. (2011) and using a

similar methodology, we projected high resolution (at 45km) changes in two temperature indices:

heating degree days (HDD) and cooling degree days (CDD), which are commonly related to

energy demand, agriculture and many other adaptation studies. We established a high resolution

statistical downscaling model for annual-accumulated HDD and CDD based on available 5

RCM/GCM pairs. We then applied this model to other GCM outputs (27 runs from 21 GCM

models) that have not yet to be downscaled to generate a high resolution probabilistic projection

for future changes in HDD and CDD. It is important to note that the output from the probabilistic

projection model provides a full spectrum of probabilistic projections (as a percentile) for both

HDD and CDD, due to a large number of GCM outputs for the downscaling processes. Similar to

the findings of Li et al. (2011) we observed large spatial variability in projected future

temperature changes, with larger temperature changes towards the north in the winter and larger

changes in the middle and lower latitudes of the USA in the summer. Sources of uncertainty in

this high resolution projection were also investigated. Under the A2 emission scenario,

downscaling from large scale to regional scale is the primary source responsible for the

uncertainty for both HDD and CDD covering the two future projected periods (2046-2065 and

2081-2100).

For Task 2, “High Resolution Climate Change Scenario on Precipitation”, we statistically

downscale GCM simulations for projected precipitation to a resolution of 45km applying a

similar methodology that Li et al. (2011) used to statistically downscale future temperature

projections. Following a similar methodology, we projected high resolution, (at 45km), changes

in monthly-accumulated precipitation. First, we established a high resolution statistical

downscaling model for monthly-accumulated precipitation. We then applied this model to output

from other GCM simulations in the same manner as HDD and CDD to generate a high resolution

probabilistic projection for future changes in precipitation by month, in a percentile basis.

We find that when applying this same approach to projected precipitation change it performs

with less than desired results than temperature or CDD/HDD, especially in the warmer months of

the year due to complex thermal processes such as deep convections. More importantly, in our

standard linear regression model, the unexplained variability is assumed to be Gaussian

distributed. Thus, the predict is itself Gaussian distributed. However, precipitation is more

commonly modeled with a gamma distribution [e.g, Katx, 1977]. However, the model did

provide some meaningful results in the case of projected precipitation change in January. This is

due to statistical downscaling having better performance in winter months than in summer

months due to complex land surface and hydrological processes in warmer months [Wetterhall et

al. 2007].

As for future work, many other approaches currently being developed model precipitation with a

Gamma, or Poisson-Gamma distribution, use weather type approaches, or stochastic weather

generators, generalized linear and additive models, and a variety of other approaches. To

employ a more appropriate method of downscaling for precipitation over North America,

particularly in Ontario, the next step requires further discussion to develop a more relevant

statistical downscaling model.

1

High Resolution Climate Change Scenario on Annual HDD and CDD

Jiafeng Wang1, Don Yu1, Longbin Chen1, Xin Qiu2, and Huaiping Zhu1

1 LAMPS, Department of Mathematics and Statistics, York University, Toronto, Ontario 2 Novus Environmental Inc., 150 Research Lane, Guelph, Ontario

1 Introduction

Current global climate models (GCMs) project a consistent increase in temperature

across North America during 21st century. On an annual basis, the warming of surface air

temperature was projected to increase 2-3°C in the southern region to more than 5°C in

the northern region of North America by the end of 2039. The largest degree of warming

could occur in winter in the northernmost region of North America due to positive

feedback from a reduced period of snow cover (IPCC 2007). The IPCC reports that most

of the increase in global average temperature can be attributed to the increase in

anthropogenic greenhouse gas (GHG) concentrations. Detectable changes due to

warming are also observed in temperature extremes (Zwiers et al. 2011) and other

components of the climate system. Due to the long effective lifetime of greenhouse gases

of current and past emissions, climate change is unavoidable (Solomon et al. 2009).

Therefore, it is necessary to adapt to the inevitable change in climate.

For government and policy makers to make adaptation plans, the information on future

climate must be provided with a level of confidence. Under IPCC different GHG

emission scenarios, global climate models (GCMs) projected the global warming for 21st

century and further (IPCC 2007). While the resolutions of most GCMs (on grid spacing

of a hundred kilometres) are coarse, the projected temperature is not spatially fine enough

for regional and local impact and adaptation studies (von Storch 2001). To downscale the

GCM projected climate change, regional climate models (RCM) can be used as a tool,

which extracts boundary forcing from GCM output and dynamically nests within GCM

domains. RCMs have finer spatial resolution (20-50 km) the GCMs and the topography

and physical processes in a region can be better simulated than GCMs. However, the cost

of RCM runs is very expensive, and it is unrealistic to apply RCMs to all regional and

local applications. On the other hand, statistical downscaling is another approach to apply

historical climate information and GCM output to estimate potential regional and local

2

climate change impact. Although the statistical downscaling method is widely used, it has

its limitations. Uncertainties due to the limits from GCMs and historical data are the main

concern. Due to the high uncertainty in regional climate change, the probabilistic

projection at high resolution is required. In the North America Regional Climate Change

Assessment Program (NARCCAP, Mearns et al. 2009), the outputs from multiple GCMs

are dynamically downscaled to high resolution over North America using multiple RCMs.

However, the current number of available RCM runs is still not adequate for probabilistic

projection.

In order to use more regional temperature change scenarios to mimic RCM simulations,

Li et al. (2011) developed an approach for high resolution probabilistic projection, which

uses output from ensembles of multiple GCMs and RCMs to produce a wide range of

plausible scenarios. Statistically downscaled models were established based on the paired

GCM-RCM temperature simulations from current years to future years. Then the

statistical relationship was applied to downscale other GCM simulations that have not yet

been dynamically downscaled by RCMs. The probabilistic projection was realized by the

empirical distribution of the downscaled high-resolution temperature projections. This

technique was applied on the seasonal mean temperature change over North America.

Large spatial variability in projected future temperature changes was found, with larger

temperature changes towards the north in the winter and larger changes in the middle and

lower latitudes of the USA in the summer. Sources of uncertainty in this high-resolution

projection were also analyzed. Under a given emission scenario, downscaling from large

scale to regional scale is the most important source responsible for the uncertainty,

though structural errors in GCMs become equally important by the end of the 21st century.

This study is an extension of the work of Li et al. (2011). Following a similar

methodology, we projected high resolution (CRCM resolution) changes in two

temperature indices: heating degree days (HDD) and cooling degree days (CDD), which

are commonly related to energy demand, agriculture and many other adaptation studies.

For example, an increase in temperature could bring serious impacts on the residential

demand for energy, which can be realized through two opposite ways: the decrease in the

use of energy for heating purposes in winter, and the increase of energy demand for

cooling purposes in summer. The demand for heating and cooling can be measured by

heating degree days (HDD) and cooling degree days (CDD). A “degree day” is a

3

measure commonly used to evaluate demand for heating and cooling services. HDDs and

CDDs are based on departures from an average temperature of 18°C, a base temperature

considered to have neither heating nor cooling needs.

In this study, we established a high resolution statistical downscaling model for annual-

accumulated HDD and CDD. We then applied this model to other GCM output to

generate a high resolution probabilistic projection for future changes in HDD and CDD.

The source of uncertainty in this high resolution projection was also investigated.

2 Data

2.1 RCM data

RCM data was downloaded from the NARCCAP website (http://www.narccap.ucar.edu/).

The model results from CRCM, RCM3, and MM5I were used in this study. CRCM was

driven by CCSM3 and CGCM3, RCM3 was driven by CGCM3 and GFDL2.1, and

MM5I was driven by CCSM3. Two time slices were provided by model simulation: 1)

1968-2000 for current climate; 2) 2038-2070 for future climate. The resolution of CRCM

is 45 km. The other RCM resolutions were re-gridded to the same resolution as the

CRCM resolution. The study domain of North America is covered by 16,100 CRCM grid

points, from 20.5 to 73.0N and from 34.0 to 160.0W.

2.2 GCM data

GCM data was downloaded from the Program for Climate Model Diagnosis and

Intercomparison (http://www-pcmdi.llnl.gov/). The GCM models used in this study are

listed in Table 1. The time span for the model output is 1) 1961-2000 for current climate;

2) 2046-2065 and 2081-2100 for projected future climates. The greenhouse gases

emission scenario for the future climate is based on the Special Report on Emissions

Scenarios combined with the A2 emission storyline (SRESA2) and the 20C3M scenario

which was run with greenhouse gases increasing as observed through the 20th century

(IPCC, 2000). Based on the available data at the time of this report for both current and

future climates, 27 runs from 21 GCMs were used in this study. All data was interpolated

into the same grid spacing of CRCM3 at 45km.

4

Table 1. GCM models in this study

Model 20C3M SRESA2 Number of runs for both 20C3M and SRESA2

ccsm3 run1, 3, 5-9 run1-5 3 gfdl2_1 run2 run1 1 bccr_bcm2_0 run1 run1 1 cccma_cgcm3_1 run1-5 run1-5 5 cccma_cgcm3_1_t63 run1 none 0 csiro_mk3_0 run1,2,3 run1 1 csiro_mk3_5 run1,2,3 run1 1 giss_aom run1 none 0 giss_model_e_h run5 none 0 giss_model_e_r run1 run1 1 iap_fgoals1_0_g run1,2,3 none 0 ingv_echam4 run1 run1 1 ipsl_cm4 run1,2 run1 1 miroc3_2_hires run1 none 0 miroc3_2_medres run1,2,3 run1,2,3 3 miub_echo_g run1,2,3 run1,2,3 3 mpi_echam5 run1,4 run1 1 mri_cgcm2_3_2a run1-5 run1-5 5 ncar_pcm1 run3,4 none 0 ukmo_hadgem1 run1 none 0 inmcm3_0 None run1 0 Total 21 Total 27

Consequently, five pairs of RCM and GCM runs (CRCM-CCSM3, CRCM-CGCM3,

RCM3-CGCM3, RCM3-GFDL2.1, and MM5I-CCSM3) were selected for this study.

3 Method

3.1 Calculation of annually accumulated HDD and CDD

The mean daily temperature is the average of eight daily temperature observations.

Historically, 18°C is chosen as the base temperature to represent human comfort level. If

the daily mean temperature T is below 18°C, heating is required and the HDD calculation

is 18°C T , which measures the departure of the temperature from human comfort level.

If the daily mean temperature T is above 18°C, the HDD for that day is zero. So, daily

HDD is calculated as follows:

5

,0

,18 THDD

.18

,18

T

T (1)

The annually accumulated HDD is the summation of daily HDD for 365 days, which is

mainly contributed in the cool seasons.

The daily CDD is derived in the same way as HDD, while in an opposite direction:

,0

,18TCDD

.18

,18

T

T (2)

The annually accumulated CDD is the summation of daily CDD for 365 days, which is

mainly contributed in the warm seasons.

3.2 Statistical Downscaling Model

Statistical downscaling was applied in this study and the methodology is the same as that

of Li et al. (2011). To bring the large-scale climate change information to a finer scale,

we used the GCM output as independent variables and the GCM-driven RCM output as

dependent variables. A time trend was also used in the regression model since there may

be some non-linearity in the responses of the RCMs that were used in the GCM forcing.

Since we were interested in the HDD/CDD changes (anomalies), the current climate

(1968-2000) mean of HDD/CDD was deducted individually by year for each RCM and

GCM run. For the purpose of HDD/CDD projection, one future time slice 2046-65 was

used together with the historical period (1968-2000) to train the statistical model to

reduce the risk from extrapolation. Changes in HDD/CDD were assumed to follow a

Gaussian distribution, thus the linear regression equation was constructed as:

xty 210 , (3)

where y is the HDD/CDD anomaly from RCM run, x is the HDD/CDD anomaly from

GCM run, t is the year for the time periods 1968-2000 and 2046-2065, 0 is intercept,

and is the regression residual ),0(~ 2 N , where is the standard deviation of the

residual.

Since we had five pairs of RCM and GCM runs (CRCM-CCSM3, CRCM-CGCM3,

RCM3-CGCM3, RCM3-GFDL2.1, and MM5I-CCSM3), five regression equations were

6

developed and used as statistical downscaling models to project the future changes in

HDD/CDD over North America.

3.3 Projected HDD/CDD changes

Following Li et al. (2011)’s approach, the newly developed statistical downscaling

models for HDD/CDD were applied to the 27 available GCM runs to develop the

ensemble of the distributions of HDD/CDD changes in 21st century under SRESA2

forcing. A total of 135 distributions for HDD/CDD changes in a given year at a give grid-

point can be generated. An empirical sampling method with 100 random numbers for

each distribution was used to project the possible changes. The 10%, 50% and 90%

percentiles were calculated from the 13,500 random values to represent the minimum,

medium, and maximum changes. The 20-year mean of the three percentiles were

calculated to demonstrate the HDD/CDD changes in the middle (2046-65) and end

(2081-2100) of the 21st century.

3.4 Uncertainty analysis

The uncertainties in statistical downscaling projection can be attributed to four sources: 1)

the selection of GCMs, 2) the selection of RCMs, or the developed regression equations

from GCM to RCM, 3) the interaction between the sources from 1) and 2), 4) the

prediction error in downscaling models. A mixed effect ‘Analysis of Variance’ (ANOVA)

model, first developed by Ronald A. Fisher, was used to estimate the contribution of each

source in the total uncertainty (Li et al. 2011). Note that mixed effects ANOVA models

have been used previously to analyse ensemble climate simulations (e.g., Zwiers, 1996).

The entire projection ensemble can be represented by

ijkijjiijkY )( , (4)

where Yijk is the final projection ensemble, is the grand mean of projection ensembles;

i is the random effect on HDD/CDD projection associated with thi GCM run

( 26,,2,1 i ); j is the random effect associated with thj regression equation

developed from GCM to RCM runs ( 5,,2,1 j ); ij)( is the random effect

associated with the combination between GCM and regression equation; and ijk is the

7

residual term, representing the uncertainty from statistical downscaling prediction error.

Assuming normality and mutual independence on random effects, the total uncertainty is

represented as

22222 , (5)

where 2 is the total projection uncertainty; 2 is the variance of i ( ),0(~ 2

Ni ;

2 , 2

, and 2 is the variance for j , ij)( , and ijk , respectively.

4 Results

4.1 Statistical downscaling model validation

The correlation coefficients for HDD/CDD between statistical downscaling projections

and RCM dynamic downscaling based on CRCM3/CGCM3 are displayed in Figure 1 a).

HDD CDD

Figure 1 a). The correlation coefficient between statistical and dynamic downscaled

HDD/CDD.

The correlation in HDD is above 0.8 almost over the entire continent. Canada and the

majority of the USA is greater than 0.9. For CDD, in the middle latitudes of North

8

America, the correlation coefficient is 0.9 and greater. The correlation coefficient is

lower in the higher latitudes of North America and ranges from 0.1 to 0.7. In Ontario, the

correlation coefficient is about 0.7 ~ 0.9 (higher in southern Ontario than northern

Ontario). The lower value in CDD can be explained by the complexity in land surface

processes in the warmer months of the year (Li et al. 2011). The RMSEs of the

statistically downscaled HDD/CDD referring to dynamically downscaled HDD/CDD

based on CRCM3/CGCM3 is displayed in Figure 1 b). The historical mean of HDD/CDD

from CRCM3/CGCM3 is also added as reference for the scale in RMSE.

The ratio of RMSE over the mean value of HDD is smaller than 1% over the entire

continent except in the southern most regions due to the smaller HDD. The ratio of

RMSE over the mean value of CDD is larger compared with HDD. Similar to figure 1 a),

the divergence is seen in northern region. The ratio is approximately 5% in the northern

regions due to the small value of CDD climate mean. The RMSE increases to about 10%

of the mean value when moving more towards to the south.

HDD RMSE CDD RMSE

Historical mean of HDD Historical mean of CDD

9

Figure 1 b). The RMSE of statistical and dynamical downscaled approaches for HDD/CDD (upper panel) and the historical mean of HDD and CDD by RCM3 (lower panel).

4.2 Projected HDD/CDD changes

Based on five pairs of RCM-GCM runs and 27 GCM climate change simulations, we

derived 135 distributions of HDD/CDD change at each year at any given grid point.

13,500 random changes were generated by implementing the bootstrap method. Among

them, the 10th, 50th and 90th percentiles of projected HDD and CDD changes were

extracted using 1968-2000 as the base period. The 20-year mean for two time slices in

21st century (2046-65 for middle century and 2081-2100 for later century) are displayed

in Figure 2 a) and b) for HDD and CDD, respectively. The figures represent the projected

change by statistical downscaling using GCM simulation as the predictor with a time

trend involved.

In Figure 2.a, the 50th percentile of projected HDD changes in 2046-2065 (central left

plot), relative to 1961-2000 climatology, range from -100 degree days in the southern

USA to -800 degree days in the Arctic area. For Ontario, the statistical downscaled

projected changes range from -400 to -800 degree days from southern Ontario to the area

surrounding Hudson Bay in the north. The 10th percentile (top left plot), which represents

the smallest changes, of HDD changes for the same time period sees a positive HDD

change in the southern regions of North America. For Ontario, the range in statistically

10

downscaled projections is between -50 and -250 degree days. The 90th percentile (bottom

left plot), which represents the maximum projected change, ranges from -200 to -1800

degree days following the same gradient direction. In Ontario, the 90th percentile

projected HDD changes range and from -800 to -1400 in 2046-2065.

For the HDD changes in the second 20 year period (2081-2100), the features are similar

to the previous 20 year period, with stronger north-south gradient. the 50th percentile of

projected HDD changes in 2081-2100 (central right plot), relative to 1961-2000

climatology, range from -100 degree days in the southern USA to -1400 degree days in

the Arctic area. For Ontario, the statistical downscaled projected changes range from -

600 to -1000 degree days from southern Ontario to the area surrounding Hudson Bay in

the north. The 10th percentile (top right), which represents the smallest changes, of HDD

changes from +50 to -600 degree days which show stronger north-south gradient than

that in the first period (2046-2065). The 90th percentile (bottom right plot), which

represents the maximum projected change, ranges from -300 to -2700 degree days

following the same gradient direction. In Ontario, the 90th percentile projected HDD

changes range and from -1000 to -1600 in 2081-2100.

The 50th percentile of projected CDD changes in 2046-2065 (Fig. 2 b), relative to 1961-

2000 climatology, range from 0 to 400 degree days. For Ontario, the range is 50 to 250

degree days. In the 10th percentile, there is more of a symmetric increase and decrease of

projected CDD changes that range from -80 to 80 degree days. The negative change is

only seen in the extreme northern part of the Arctic. For the majority of the continent,

the CDD changes are positive. The centers of negative CDD change are observed in the

Midwestern USA, and extend northwest to the Great Plateau in western Canada. The

increase is seen in the southwestern USA and the northern part Mexico. For Ontario, the

minimum projected CDD changes are between 0 and 60 degree days. For the 90th

percentile of projected CDD changes over North America, the range is between 100 and

1100 degree days.

As shown in Fig 2.b, the patterns of CDD changes in the second 20 year period (2081-

2100 are similar to the previous 20-year period, but with a “warmer” tendency, i.e.,

positive changes in CDD are increased than the first 20-year period. The 50th percentile

of projected CDD changes in 2081-2100 (central right plot), relative to 1961-2000

11

climatology, range from 100 degree days in the Arctic area to 800 degree days in the

southern USA. For Ontario, the statistical downscaled projected changes range from 100

to 400 degree days from the area surrounding Hudson Bay to southern Ontario.

Particularly for the 90th percentile (bottom right plot), which represents the maximum

projected change, ranges from 300 to 2000 degree days with strong gradient from central

USA to southern USA.

The results are summarized in Table 2.

Table 2) Projected HDD/CDD changes by statistical downscaling for 2046-2065 and 2081-2100

Changes in HDD/CDD in Degree Days

North America HDD CDD Big change in the North; small

change in the South Big change in the South; small change in the North

2046-2065 2081-2100 2046-2065 2081-2100 Minimum -300 ~ +100 -800 ~ 0 -80 ~ +80 0 ~ +240 Medium -800 ~ -100 -1600 ~ -200 0 ~ +400 +100 ~ +800 Maximum -1800 ~ -200 -2700 ~ -300 +100 ~ +1100 +300 ~ +2000

Ontario

HDD CDD Big change in the North; small

change in the South Big change in the South; small change in the North

2046-2065 2081-2100 2046-2065 2081-2100 Minimum -250 ~ -50 -600 ~ -200 0 ~ +60 +30 ~ +150 Medium -800 ~ -400 -1400 ~ -600 +50 ~ +250 +100 ~ +400 Maximum -1400 ~ -800 -2100 ~ -1200 +100 ~ +500 +200 ~ +1000

12

Statistical Downscaling HDD changes in 2046-2065 HDD changes in 2081-2100

Figure 2 a) The projected changes in HDD from statistical downscaling in 2046-65 (left column) and 2081- 2100 (right column). The top row represents the minimum change, middle for medium change, and bottom for maximum change, i.e. 10th, 50th, and 90th percentiles respectively. (Units in Degree Days)

13

Statistical Downscaling CDD changes in 2046-2065 CDD changes in 2081-2100

Figure 2 b). The same as a), but for CDD changes in 2046-2065 (left column) and 2081-2100(right column).

14

4.3 Source of uncertainty

The contribution of the uncertainty sources (GCM, regression equation (RE), interaction

of GCM and RE (GCM*RE), statistical downscaling prediction error (RES)) are analysed

by two-way ANOVA analysis and the percentage of each factor contributing to the total

uncertainty over North America is displayed in Figure 3.

Figure 3. Percentage (×100%) of different factors contributing to the total uncertainty.

We observe that the regression equation (RE) takes the majority of uncertainty in HDD

projection, and its weight increases with time up to 60%. The contribution from GCM is

lower than 20%, and a slight reduction is seen from 2046-2065 to 2081-2100. The

random effects of the interaction between GCM and regression equation is almost the

same for the two periods, and the variance of residual is smaller in the later period.

Among the four factors, the uncertainty from RE is responsible for the majority of

uncertainty in both periods. The contribution of GCM selection jumps from the third rank

to the second, while the residual’s contribution drops from the second to the last, almost

in the same level as the interaction between GCM and RE. For CDD, the uncertainty

from RE increases with time and is responsible for the majority of uncertainty for both

periods. The contribution from GCM selection increases as well, but remains well under

20% for both periods. However, for CDD, uncertainty attributed to GCM is larger than

that of HDD for both periods. The contribution of interaction between GCM and RE

increases as well, but it is still smaller than the percentage of RES contribution for both

periods.

15

5 Conclusion and Discussion

Using the RCM and GCM projected change in temperature, the high resolution

probabilistic projection model for HDD/CDD changes over North America has been

developed by using statistical downscaling in the framework of a linear regression model.

The projected change in HDD/CDD and their uncertainties are displayed in figure 3 for

the middle and later 20-year periods in the 21st century. We observe a decrease of HDD

over time and the rate of decrease increases from south to north. The largest reduction of

HDD is in the northern part of North America. For Ontario, based on the 50th percentile,

the median level of projected HDD change is from -800 ~ -400 degree days for 2046-

2065 to -1400 ~ -600 degree days for 2081-2100. The major changes in northern Ontario

and minor changes in southern Ontario could imply the heating demand could decrease in

the future with geographical variation. Similarly, we expect to see an increase in CDD

with time. The increasing gradient is from the north to the south over North America, as

opposed to HDD. For Ontario, the 50th percentile of projected CDD increase is from 50 ~

250 degree days for 2046-2065 and 100 ~ 400 degree days for 2081-2100 which is

smaller in magnitude than changes in HDD for the same two periods. The largest increase

is found in southern Ontario and smallest increase is found in northern Ontario. Based on

the 50th percentile for both periods, the great unbalance in the decrease in HDD and

increase in CDD in northern Ontario, the projected climate change could mean a potential

cost savings in energy to the remote area assuming the cost of cooling is less than the cost

of heating. While, for the heavily populated southern Ontario, the increase in CDD

almost offsets the decrease in HDD. The uncertainty in HDD/CDD projection is mainly

from the trained relationship between GCM and RCM simulations, followed by GCM

selection or interaction between GCM and regression relation. The uncertainty in CDD is

more diverse among the factors than the uncertainty in HDD, due to the complex land

surface processes in the summer time. This study has shown that the high resolution

probabilistic projection by statistical downscaling could provide useful information on

HDD/CDD changes, which could be used by policy makers on energy planning at a

regional scale.

16

Acknowledgement

This work is supported by Ministry of Environment of Ontario, ERA an early researcher

award of Ontario and CFI. We appreciate Drs. Xuebin Zhang, Guilong Li, Peter Taylor,

Kaz Higuchi, Rick Bello and Georges Monette for their helpful discussions. Thanks for

Dr. Guilong Li for providing the partial data and computing code of his research.

17

Reference

IPCC, 2007. Climate Change. Cambridge University Press, 890pp.

Li, G., X. Zhang, F. Zwiers, H. Qiuzi, 2011. Quantification of uncertainty in high

resolution temperature scenarios for North America. Submitted to Journal of Climate.

Mearns, L. O., W. J. Gutowski, R. Jones, L.-Y. Leung, S. McGinnis, A. M. B. Nunes, Y.

Qian, 2009: A regional climate change assessment program for North America. EOS,

90, 311-312.

Solomon, S., G. K. Plattner, R. Knutti, and P. Friedlingstein, 2009: Irreversible climate change due to carbon dioxide emissions. Proc. Natl Acad. Sci. USA 106, 1704–1709.

von Storch, H., 2001: Models. In: H. von Storch and G. Flöser (Eds): Models in

Environmental Research. Springer Verlag, 17-33 Zwiers, F. W., 1996: Interannual variability and predictability in an ensemble of AMIP

climate simulations conducted with the CCC GCM2. Clim. Dyn., 12, 825-847. Zwiers, F. W., X. Zhang, Y. Feng, 2011: Anthropogenic influence on long return period

daily temperature extremes at regional scales. Journal of Climate, doi:10.1175/2010JCLI3908.1.

1

High Resolution Climate Change Scenario on Precipitation

Don Yu1, Longbin Chen1, Xin Qiu2, Jiafeng Wang1, and Huaiping Zhu1

1 LAMPS, Department of Mathematics and Statistics, York University, Toronto, Ontario 2 Novus Environmental Inc., 150 Research Lane, Guelph, Ontario

1 Introduction

Global climate models (GCMs) are the primary tool for understanding how the global

climate may change in the future. However, these currently do not provide reliable

information on scales below about 200 km [Meehl et al., 2007]. Hydrological processes

typically occur on finer scales [Kundzewicz et al., 2007]. In particular, GCMs cannot

resolve circulation patterns leading to hydrological extreme events [Christensen and

Christensen, 2003]. Hence, to reliably assess hydrological impacts of climate change,

higher-resolution scenarios are required for the most relevant meteorological variables

[Maraun et al, 2009].

There are two main approaches of downscaling. Dynamic downscaling nests a Regional

Climate Model (RCM) into the driving GCM to generate climate projections at a finer

resolution than GCMs. Statistical downscaling establishes statistical relationships

between paired GCM-RCM simulations and then applies those statistical relationships to

output from other GCMs that have not yet been downscaled by RCMs.

Although the statistical downscaling method is widely used, it has its limitations.

Uncertainties due to the limits from GCMs and historical data are the main concern. Due

to the high uncertainty in regional climate change, probabilistic projection at high

resolution is required. In the North America Regional Climate Change Assessment

Program (NARCCAP, Mearns et al. 2009), the outputs from multiple GCMs are

dynamically downscaled to high resolution over North America using multiple RCMs.

However, the current number of available RCM runs is still not adequate enough for

probabilistic projection.

In this study, we statistically downscale GCM simulations for projected precipitation to a

resolution of 45km applying a similar methodology that Li et al. (2011) used to

2

statistically downscale future temperature projections. Li et al. (2011) developed an

approach for high resolution probabilistic projection, which uses output from ensembles

of multiple GCMs and RCMs to produce a wide range of plausible scenarios. Statistically

downscaled models were established based on the paired GCM-RCM temperature

simulations from current years to future years. Then the statistical relationship was

applied to downscale other GCM simulations that have not yet been dynamically

downscaled by RCMs. The probabilistic projection was realized by the empirical

distribution of the downscaled high-resolution temperature projections. Their technique

was applied on the seasonal mean temperature change over North America.

This study is an extension of the work of Li et al. (2011). Following a similar

methodology, we projected high resolution (CRCM resolution) changes in monthly-

accumulated precipitation. First, we established a high resolution statistical downscaling

model for monthly-accumulated precipitation. We then applied this model to output from

other GCM simulations to generate a high resolution probabilistic projection for future

changes in precipitation. The source of uncertainty in this high resolution projection was

also investigated.

We find that when applying this same approach to projected precipitation change it

performs with less than desired results, especially in the warmer months of the year due

to complex land surface and hydrological processes. More importantly, in our standard

linear regression model, the unexplained variability is assumed to be Gaussian distributed.

Thus, the predictand is itself Gaussian distributed. However, precipitation is more

commonly modeled with a gamma distribution [e.g, Katx, 1977]. We also discuss

advantages and drawbacks of other statistical downscaling approaches that could produce

more credible results with less probabilistic uncertainty.

2 Data

2.1 RCM data

RCM data was downloaded from the NARCCAP website (http://www.narccap.ucar.edu/).

The model results from CRCM and RCM3 were used in this study. CRCM was driven by

CCSM3 and CGCM3, RCM3 was driven by CGCM3 and GFDL2.1. Two time slices

3

were provided by model simulation: 1) 1968-1998 for current climate; 2) 2046-2065 for

future climate. The resolution of CRCM is 45 km. The other RCM resolutions were re-

gridded to the same resolution as the CRCM resolution. The study domain of North

America is covered by 16,100 CRCM grid points, from 20.5 to 73.0N and from 34.0 to

160.0W.

2.2 GCM data

GCM data was downloaded from the Program for Climate Model Diagnosis and

Intercomparison (http://www-pcmdi.llnl.gov/). The GCM models used in this study are

listed in Table 1. The time span for the model output is 1) 1968-1998 for current climate;

2) 2046-2065 and 2081-2100 for projected future climates. The greenhouse gases

emission scenario for the future climate is based on the Special Report on Emissions

Scenarios combined with the A2 emission storyline (SRESA2) and the 20C3M scenario

which was run with greenhouse gases increasing as observed through the 20th century

(IPCC, 2000). Based on the available data at the time of this report for both current and

future climates, 26 runs from 21 GCMs were used in this study. All data was interpolated

into the same grid spacing of CRCM3 at 45km.

Table 1. GCM models in this study

Model 20C3M SRESA2 Number of runs for both 20C3M and SRESA2

ccsm3 run1, 3, 5-9 run1-5 3 gfdl2_0 run1 run1 1 gfdl2_1 run2 run1 1 bccr_bcm2_0 run1 run1 1 cccma_cgcm3_1 run1-5 run1-5 5 cccma_cgcm3_1_t63 run1 none 0 csiro_mk3_0 run1,2,3 run1 0 csiro_mk3_5 run1,2,3 run1 1 giss_aom run1 none 0 giss_model_e_h run5 none 0 giss_model_e_r run1 run1 1 iap_fgoals1_0_g run1,2,3 none 0 ingv_echam4 run1 run1 1 ipsl_cm4 run1,2 run1 1 miroc3_2_hires run1 none 0 miroc3_2_medres run1,2 run1,2 2 miub_echo_g run1,2,3 run1,2,3 3

4

mpi_echam5 run1,4 run1 1 mri_cgcm2_3_2a run1-5 run1-5 5 ncar_pcm1 run3,4 none 0 ukmo_hadgem1 run1 none 0 inmcm3_0 None run1 0 Total 21 Total 26

Consequently, four pairs of RCM and GCM runs (CRCM-CCSM3, CRCM-CGCM3,

RCM3-CGCM3, and RCM3-GFDL2.1) were selected for this study.

3 Method

3.1 Calculation of Monthly Accumulated Precipitation

For the four pairs of RCM/GCM output, the daily precipitation was calculated as the sum

of eight daily precipitation observations. The monthly accumulated precipitation is then

calculated based on the sum of the daily precipitation for each month. Monthly data for

GCMs was downloaded at the Program for Climate Model Diagnosis and

Intercomparison’s website.

3.2 Statistical Downscaling Model

The methodology used for statistical downscaling in this study is similar to that used by

Li et al. (2011) for seasonal temperature projections. To bring the large-scale climate

change information to a finer scale, we used the GCM output as independent variables

and the GCM-driven RCM output as dependent variables. A time trend was also used in

the regression model since there may be some non-linearity in the responses of the RCMs

that were used in the GCM forcing. Since we were interested in the change in

precipitation (anomalies), the current period (1968-1998) mean of precipitation was

deducted individually by month for each RCM and GCM run. For the purpose of monthly

accumulated precipitation projection, one future time slice 2046-2065 was used together

with the historical period 1968-2000 to train the statistical model to reduce the risk from

extrapolation. Changes in precipitation were assumed to follow a Gaussian distribution,

thus the linear regression equation was constructed as:

xty 210 , (3)

5

where y is the precipitation anomaly from RCM run, x is the precipitation anomaly

from GCM run, t is the year for the time periods 1968-1998 and 2046-2065, 0 is

intercept, and is the regression residual ),0(~ 2 N , where is the standard

deviation of the residual.

Since we had four pairs of RCM and GCM runs (CRCM-CCSM3, CRCM-CGCM3,

RCM3-CGCM3, and RCM3-GFDL2.1), four regression equations were developed and

used as statistical downscaling models to project the future changes in precipitation over

North America.

3.3 Projected Precipitation Changes

Following Li et al. (2011)’s approach, the newly developed statistical downscaling

models for precipitation were applied to the 26 available GCM runs to develop the

ensemble of the distributions of precipitation changes in 21st century under SRESA2

forcing. A total of 130 distributions for precipitation changes in a given year at a given

grid-point can be generated. An empirical sampling method with 100 random numbers

for each distribution was used to project the possible changes. The 10%, 50% and 90%

percentiles were calculated from the 13,000 random values to represent the minimum,

medium, and maximum changes. The 20-year mean of the three percentiles were

calculated to demonstrate the precipitation changes in the middle (2046-65) and end

(2081-2100) of the 21st century.

3.4 Uncertainty analysis

The uncertainties in statistical downscaling projection can be attributed to four sources: 1)

the selection of GCMs, 2) the selection of RCMs, or the developed regression equations

from GCM to RCM, 3) the interaction between the sources from 1) and 2), 4) the

prediction error in downscaling models. A mixed effect ‘Analysis of Variance’ (ANOVA)

model, first developed by Ronald A. Fisher, was used to estimate the contribution of each

source in the total uncertainty (Li et al. 2011). Note that mixed effects ANOVA models

have been used previously to analyse ensemble climate simulations (e.g., Zwiers, 1996).

The entire projection ensemble can be represented by

6

ijkijjiijkY )( , (4)

where Yijk is the final projection ensemble, is the grand mean of projection ensembles;

i is random effect on precipitation projection associated with thi GCM run

( 26,,2,1 i ); j is random effect associated with thj regression equation developed

from GCM to RCM runs ( 4,,2,1 j ); ij)( is the random effect associated with the

combination between GCM and regression equation; and ijk is the residual term,

representing the uncertainty from statistical downscaling prediction error. Assume

normality and mutual independence on random effects, the total uncertainty is

represented as

22222 , (5)

where 2 is the total projection uncertainty; 2 is the variance of i ( ),0(~ 2

Ni ;

2 , 2

, and 2 is the variance for j , ij)( , and ijk , respectively.

4 Results

4.1 Statistical Downscaling Model Validation

The correlation coefficients for precipitation projections in January and July between

statistical downscaling projections and dynamic downscaled RCM projections based on

CRCM3/CGCM3 are displayed in Figure 1 a).

7

January July

Figure 1 a). The correlation coefficient between statistical and dynamic downscaled precipitation projections for January

and July based on CRCM/CGCM3.

The correlation coefficient for January is above 0.9 along the west coast of North

America as well as in some states in the south and southwest of the USA. In some

regions in southern Canada and northern USA the correlation decreases significantly to

0.3. The rest of the continent has a correlation coefficient ranging from 0.65 to 0.85.

This implies a high correlation between the CRCM simulation and the driving GCM

mostly on the western coastline, but low correlation elsewhere. In July, there is only a

very small region in the northwest of the USA that has a coefficient above 0.8. The rest

of the continent ranges from 0 to 0.75. Ontario has a correlation coefficient ranging from

0.1 to 0.55 in July. Correlation coefficients in January tend to more highly correlated

than those of July. In winter months the a large portion of the land surface is covered by

snow or is frozen thereby isolating the atmosphere from the land surface, whereas the

land surface is more strongly coupled to the atmosphere in summer. This results in

stronger influence of large scale variations on small scale variations in precipitation in

winter than in summer, and thus a better overall match between large-scale and small

scale variability in winter (Li et al 2011). We predict statistical downscaling would have

a higher level or correlation if we were to model the change in precipitation as a Gamma

distribution.

8

The RMSEs between statistically and dynamically downscaled precipitation based on

CRCM/CGCM3 for January and July are displayed in Figure 1 b).

January RMSE July RMSE

Figure 1 b). The RMSE for January and July between statistically and dynamically downscaled precipitation projections

based on CRCM/CGCM3.

RMSEs for range from 0 to 36 for both January and July. Larger RMSEs indicate larger

predictive uncertainty. We observe larger RMSEs in the southern and eastern states of

the USA and mostly in the eastern provinces of Canada, especially during July.

4.2 Projected Precipitation Changes

Based on four pairs of RCM-GCM runs and 26 climate change simulations conducted by

GCM runs, we derived 104 distributions of precipitation change at each month at any

given grid point. 10,400 random changes were generated by implementing the bootstrap

method. Among them, the 10th, 50th and 90th percentiles of projected precipitation

changes were extracted using 1968-1998 as the base period. The 20-year mean for the

mid and late 21st century (2046-2065 for middle century and 2081-2100 for later century)

are displayed in Figures 2 a) and b).

9

Projected change of monthly accumulated precipitation in January for North America (Units: mm)

2046-2064 p10 2081-2100 p10

2046-2064 p50 2081-2100 p50

2046-2064 p90 2081-2100 p90

Figure 2 a) The 20-yr averages of the 10th, 50th, and 90th percentiles for the projected changes in monthly precipitation for January from statistical downscaling in 2046-2064 and 2081-2100 based on SRES-A2 emission scenario.

10

Projected change of monthly accumulated precipitation in July for North America (Units: mm)

2046-2064 p10 2081-2100 p10

2046-2064 p50 2081-2100 p50

2046-2064 p90 2081-2100 p90

Figure 2 b) The 20-yr averages of the 10th, 50th, and 90th percentiles for the projected changes in monthly precipitation for July from statistical downscaling in 2046-2064 and 2081-2100 based on SRES-A2 emission scenario..

11

In general, precipitation increases tend to be greater at high latitudes in the January. The

50th percentile of projected precipitation changes in 2046-2065 for the month of January

(Fig. 2 a), relative to 1968-1998 climatology, range from -20 mm in the southern region

of the USA and Mexico to 20 mm in the northwestern and northeastern regions of the

USA and Canada. The Midwestern states as well as central Canada and the arctic have a

projected increase from 0 to 5 mm. For Ontario, the statistically downscaled projected

precipitation changes range from 0 to 5 mm in western Ontario and from 5 to 10 mm in

central and eastern Ontario. In the later period, 2081-2100, the projected precipitation

change closely resembles the distribution of precipitation change of the previous period.

However, for a small area in south eastern Alaska and south western Yukon Territory we

observe a projected change of up to 50 mm. For the 10th percentile, which represents the

smallest changes, we observe a dramatic decrease in precipitation change over North

America ranging from -10 to -80 mm over both projected periods. For Ontario, the range

in projections are between -10 and -30 mm. At the 90th percentile, which represents the

maximum projected change, there is a large increase in projected precipitation change

ranging from 10 to 80 mm. In general we observe larger changes in precipitation along

the coastal regions of the continent for January. The difference between the 90th and 10th

percentiles share a close resemblance for both periods, indicating a similar level of

uncertainty in projected precipitation change for both periods towards the more remote

future.

During July, the change in projected precipitation for the 50th percentile ranges from -40

to 30 mm for both periods with increases in precipitation observed more in northern

Canada while decreases tend to be in the USA. The spatial distribution of precipitation

for all three percentiles bear a close resemblance from one period to the next. The range

in projected precipitation change from the 10th to 90th percentile is of 140 mm in

magnitude which suggests a high degree of uncertainty in the projected change for both

periods.

The projected precipitation change data for the two periods 2046-2065 and 2081-2100 is

summarized in Table 1.

12

Projected Change in Precipitation (Units: mm)

North America

January July 2046-2065 2081-2100 2046-2065 2081-2100 Minimum -80 ~ +5 -80 ~ +5 -80 ~ -30 -80 ~ -30 Medium -20 ~ +20 -20 ~ +50 -20 ~ +20 -30 ~ +50 Maximum 0 ~ +80 0 ~ +80 +5 ~ +80 +5 ~ +80

Ontario

January July 2046-2065 2081-2100 2046-2065 2081-2100 Minimum -30 ~ -10 30 ~ -10 -80 ~ -40 -80 ~ -40 Medium 0 ~ +10 0 ~ +20 -10 ~+ 5 -20 ~ +10 Maximum +10 ~ +70 +20 ~ +70 +50 ~ +80 +50 ~ +80 Table 1) Projected precipitation changes by statistical downscaling for 2046-2065 and 2081-2100

4.3 Source of Uncertainty

The contribution of sources of uncertainty (GCM, regression equation (RE), interaction

of GCM and RE (GCM*RE), statistical downscaling prediction error (RES)) are analysed

by two-way ANOVA analysis and the percentage of each factor contributing to the total

uncertainty over North America is displayed in Figure 3.

Figure 3. Percentage (×100%) of different factors contributing to the total uncertainty.

We observe that the GCM is responsible for the majority of uncertainty in projected

precipitation change in January, and its weight decreases slightly over the next period

The contribution from RE is lower than 5% for both periods. The random effects of the

interaction between GCM and regression equation are almost the same for the two

periods, around 32%, and the variance of residual is around 10% for both periods.

Among the four factors, the uncertainty from GCM is responsible for the majority of

13

uncertainty in both periods. For July, the weight in contribution of GCM and interaction

between GCM and regression equation are reversed. The interaction between GCM and

regression equation is now responsible for the majority of uncertainty at 50% and 48%

for both projected periods 2046-2065 and 2081-2100, respectively. The contribution of

GCM selection is slightly above 30% for both periods, while the residual’s contribution is

approximately equal to that of January for both periods. Similar to January, the regression

equation RE contributes the least amount of uncertainty.

5 Conclusion and Discussion

We developed a high resolution probabilistic projection model for precipitation changes

over North America by using statistical downscaling in the framework of a linear

regression model. Empirical distributions for projected precipitation change were then

estimated based on the application of statistical relationships between four pairs of GCM-

RCM simulations. Sources of uncertainty were also investigated.

Immediately we observed an overall low level of correlation between CRCM/CGCM3 as

well as significantly high RMSEs over North America for January and July in both

projected periods. This implies the use of a Gaussian distribution is not as ideally suited

for statistically downscaling precipitation as it is for temperature. We believe the main

factor contributing to the low level of correlation is the assumption that the large scale

predictand is Gaussian. However, our model did provide some meaningful results in the

case of projected precipitation change in January. Statistical downscaling performs better

in winter months than in summer months due to complex land surface and hydrological

processes in warmer months [Wetterhall et al. 2007]. Even with the Gaussian assumption

in our model we observe this to be the case, as shown in Figure 1 a), which is likely

because a large portion of the land surface is covered by snow or is frozen thereby

isolating the atmosphere from the land surface. A key source of model deficiencies in the

simulation of precipitation is the convective parameterization. In particular, many of the

parameterization schemes used in RCMs may not be appropriate, having been developed

for coarser-resolution GCMs and tropical regions [Hohenegger et al. 2008]. This is

particularly likely to be an issue in summer, when rainfall is predominantly convective in

nature and on subdaily time scales [Lenderink and van Meijgaard, 2008]

14

Many other approaches currently being developed model precipitation with a Gamma, or

Poisson-Gamma distribution, use weather type approaches, or stochastic weather

generators, generalized linear and additive models, and a variety of other approaches (not

named here) [Maraun et al, 2009]. Groppelli et al. (2010) used a Stochastic Space

Random Cascade approach to downscale precipitation an Italian Alpine watershed, the

Oglio river. However, they locally tuned the approach upon the Oglio river based on a

10year series of observed daily precipitation data from 25 rain gages. In general, the

most relevant meteorological variables for hydrological impact studies are precipitation

and temperature [Xu, 1999b; Bronstert et al., 2007]. For freshwater resources in

particular, precipitation is the most important driver [Kundzewicz et al., 2007], though it

is considerably more difficult to model than temperature mostly because of its high

spatial and temporal variability and its nonlinear nature [Maraun et al, 2009].

In this study we assumed the unexplained variability was Gaussian distributed in order to

identify the deficiencies in this particular statistical downscaling approach. To employ a

more appropriate method of downscaling for precipitation over North America,

particularly in Ontario, the most important step is to develop a more relevant statistical

downscaling model. Due to Ontario’s close proximity to the Great Lakes and its unique

geographical properties there must be more discussion and research as to how we can

further develop a statistical downscaling approach to accomplish this challenge.

Acknowledgements

This work is supported by Ministry of Environment of Ontario, ERA an early researcher

award of Ontario and CFI. We appreciate Drs. Xuebin Zhang, Guilong Li, Peter Taylor,

Kaz Higuchi, Rick Bello and Georges Monette for their helpful discussions. Thanks for

Dr. Guilong Li for providing the partial data and computing code of their research.

15

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