Embed Size (px)
Citation preview
1
Statistical Downscaling of 1
Wintertime Temperatures over South Korea 2
3
Seoyeon Lee and Kwang-‐Yul Kim 4
School of Earth and Environmental Sciences, Seoul National University 5
Seoul, 151-‐747, Republic of Korea 6
7
8
9
* Corresponding author: Kwang-‐Yul Kim ([email protected]) 10
School of Earth and Environmental Sciences, Seoul National University 11
1 Gwanangno, Gwanak-‐gu, Seoul, 151-‐747, Republic of Korea 12
+82-‐2-‐880-‐4205 (phone), +82-‐2-‐883-‐4972 (fax) 13
Submitted to: Journal of Atmospheric and Oceanic Technology 14
Submission date: January 8, 2015 15
2
Abstract 16
Reanalysis data have global coverage and faithfully render large-‐scale 17
phenomena. On the other hand, regional and small-‐scale characteristics of 18
atmospheric variability are poorly resolved. In an attempt to improve reanalysis 19
data for regional use, statistical downscaling strategy is developed based on 20
Cyclostationary Empirical Orthogonal Function (CSEOF) analysis. The developed 21
algorithm is applied to the National Center for Environmental Prediction-‐22
National Center for Atmospheric Research (NCEP/NCAR) reanalysis data and the 23
European Center for Medium Range Weather Forecast (ECMWF) ERA-‐interim 24
reanalysis data in order to produce winter temperatures at 60 Korea 25
Meteorological Administration (KMA) stations over the Korean Peninsula. The 26
developed downscaling algorithm is evaluated by predicting winter daily 27
temperatures from Nov. 17–Mar. 16 for the period of 35 years (1979-‐2014). For 28
validating the downscaling algorithm the Jackknife method is used, in which 29
winter daily temperature is predicted over a one-‐year period not used for 30
training. This procedure is repeated for the entire data period. Mean and 31
variance of the resulting downscaled temperatures match reasonably well with 32
those of the KMA measurements. Validation based on correlation and error 33
variance shows that the temperatures at 60 KMA stations are faithfully 34
reproduced based on coarse reanalysis data. The utility of this technique for 35
downscaling model predictions based on future scenarios is also addressed. 36
3
1. Introduction 37
General circulation models (GCMs) are a widespread means of 38
understanding future climate and various aspects of climate changes (Hansen et 39
al. 1988; Cox et al. 1999; Murphy et al. 2004; IPCC 2013). They also serve as a 40
useful tool for seasonal forecasts and long-‐term predictions. Considerable effort 41
to improve the performance of GCMs has been made for the past decades and 42
GCMs are capable of simulating large-‐scale climatological features and their 43
changes in the atmosphere and the oceans. One important factor in improving 44
GCMs is the temporal and spatial resolution of the model (IPCC 1996; Sakamoto 45
et al. 2004; Kimoto et al. 2005; IPCC 2007). Interaction of climatological features 46
across different scales should be simulated properly in order to make reliable 47
long-‐term prediction of climates (Palmer et al. 2008; Shukla 2009; Hoskins 48
2013). 49
While the resolution of GCMs has significantly increased and is still 50
increasing, the present generation of general circulation models (GCMs) has not 51
yet reached a level of resolution sufficient for simulating small regional features. 52
The current computational power does not yet allow GCMs with, say, a 1-‐km 53
resolution over the whole earth. In order to capture small regional features, 54
dynamical downscaling method has been used frequently, in which a high-‐55
resolution model with a smaller spatial domain is imbedded in a low-‐resolution 56
GCM. This so-‐called “nesting” is often conducted a few times to accomplish 57
model computations at a desirable resolution (Giorgi 1990; Ji and Vernekar 1997; 58
Fennessy and Shukla 2000; Jones et al. 1995). Dynamical downscaling method 59
has been applied to specific areas to address regional features (Giorgi 1990; Ji 60
and Vernekar 1997; Fennessy and Shukla 2000; Misra et al. 2003; Coulibaly et al. 61
4
2005; Sun et al. 2006; Lim et al. 2007). While dynamical downscaling techniques 62
have proven to be useful and provided local conditions in greater detail, they 63
also suffer from the difficulty of prescribing open boundary conditions (Giorgi 64
1990; Jones et al. 1995; Christensen et al. 1997; Marchesiello et al. 2001). A 65
regional climate model (RCM) simulation is often inadvertently affected in a 66
significant manner by natural variability in a GCM output introduced through 67
open boundary conditions. 68
Statistical downscaling is also common and is a simple alternative to 69
dynamical downscaling (Hewitson and Crane 1996; Wilby and Wigley 1997; 70
Wilby et al. 1998; Wilks 1999; Huth and Kysely 2000; Huth 2002; Widmann et al. 71
2003; Robertson et al. 2004; Feddersen and Andersen 2005; Lim et al. 2007) or 72
serves a means of improving dynamical downscaling (Fuentes and Heimann 73
2000). As the name implies, statistical downscaling delves into statistical 74
relationship between two variables—often between a large-‐scale feature such as 75
atmospheric pressure and a local feature such as wind speed at a specific 76
location—in order to draw inference on a local feature based on a large-‐scale 77
feature (Wilby et al. 2004; Lim et al. 2007). In this way, low-‐resolution GCM 78
output can be used to obtain detailed local features. As such, statistical 79
downscaling method can bridge the gap between coarse GCM outputs and 80
detailed regional outputs necessary for environmental assessment and decision 81
making (Wilby and Wigley 1997; Huth and Kysely 2000). Statistical downscaling, 82
of course, is computationally much more efficient than dynamical downscaling. 83
South Korea is located in the eastern coast of Asia and is strongly 84
influenced by the East Asian winter monsoon (EAWM) during winter. A strong 85
EAWM is characterized as strong low-‐level northwesterlies and the ensuing cold 86
5
surface air temperatures over the northeastern part of East Asia, including 87
northeastern China, Korea, and Japan. Although South Korea occupies a small 88
region, wintertime daily temperatures are highly variable due to its geographic 89
location and topographic complexity. Thus, GCMs have difficulty resolving 90
detailed regional features over the Korean peninsula, and an accurate 91
downscaling method proves to be useful. In this study, a statistical downscaling 92
method is developed based on CSEOF analysis (Kim et al. 1996; Kim and North 93
1997) for the purpose of improving GCM outputs to reflect regional details over 94
the Korean peninsula. 95
The paper is organized as follows. Section 2 provides information on the 96
datasets used for this study. Section 3 addresses the concept of statistical 97
downscaling technique based on CSEOF analysis. Then, the accuracy and utility 98
of the developed downscaling method is discussed in section 4 in terms of 99
various statistical measures. Finally, summary and concluding remarks follow in 100
section 5. 101
102
2. Data 103
This study uses winter 120-‐day (Nov. 17 – Mar. 16) Korea Meteorological 104
Administration (KMA) daily mean temperature measured at 60 stations (Fig. 1) 105
for a 35-‐year period (1979/1980-‐2013/2014). One KMA station, Andong, was 106
excluded in this study, since it has an incomplete record for the 35-‐year period. 107
The KMA measurements have relatively high resolution, which is used as the 108
target variable in this study. 109
Winter temperatures at surface (2 m), 1000, and 850 hPa from the 110
National Center for Environmental Prediction-‐National Center for Atmospheric 111
6
Research (NCEP/NCAR) reanalysis dataset (Kalnay et al. 1996) have relatively 112
low resolution: T62 Gaussian grid with 192×94 points for surface data and 113
2.5°×2.5° resolution for pressure level data. The dashed lines in Fig. 1 represent 114
the latitude-‐longitude grids of the NCEP/NCAR reanalysis surface temperature. 115
The four red dots denote the KMA stations closest to the NCEP/NCAR grid points. 116
The 1.5°×1.5° ERA interim reanalysis daily temperatures at surface (2 m), 1000 117
and 850 hPa from the European Center for Medium Range Weather Forecast 118
(ECMWF) are also used in this study (Dee et al. 2011). Both reanalysis data are 119
for the same period of time of the KMA data and cover South Korea [31.4°-‐40.0°N, 120
124.5°-‐132.5°E]. These lower-‐resolution temperatures serve as the predictor 121
variables based on which a downscaling method will be developed to estimate 122
the target variable (the KMA temperatures). 123
124
3. Method of Analysis 125
3.1. Cyclostationary EOF (CSEOF) Analysis 126
Given a space-‐time dataset, Data(r,t) , cyclostationary empirical 127
orthogonal function (CSEOF: Kim et al. 1996; Kim and North 1997) analysis 128
decomposes them into 129
Data(r,t) = CSLVn (r,t)PCn (t)n∑ , t ∈D , (1) 130
where CSLVn (r,t) are the n th cyclostationary loading vectors (CSLV), PCn (t) 131
are corresponding principle component (PC) time series and D is the record 132
length of the data. Each CSLV is periodic in time with the nested period d , which 133
is set to 120 days in the present study. Thus, 134
7
CSLVn (r,t) = CSLVn (r,t + d) , (2) 135
and each CSLV describes a deterministic evolution of temperature during winter. 136
The corresponding PC time series represents longer-‐term variation of the 137
amplitude of the evolution depicted in the loading vector. Details of CSEOF 138
analysis are referenced to Kim et al. (1996), Kim and North (1997), and Kim and 139
Wu (1999). 140
The KMA measurement (target variable) and the reanalysis temperature 141
(predictor variable) can be written as 142
T (r,t) = Bn (r,t)Tn (t)n∑ , t ∈D , (3) 143
and 144
P(r,t) = Cn (r,t)Pn (t)n∑ , t ∈D , (4) 145
where Bn (r,t) and Cn (r,t) are respectively the CSLVs of the target and the 146
predictor variables, and Tn (t) and Pn (t) are corresponding PC time series. 147
148
3.2. Regression Analysis in CSEOF Space 149
Two sets of CSEOFs derived from the target and predictor variables do 150
not exhibit one-‐to-‐one correspondence. Namely, two PC time series for each 151
mode number n are not maximally correlated. The two corresponding loading 152
vectors, as a result, do not necessarily have identical amplitude variation. In 153
order to make two sets of CSEOFs physically consistent, therefore, regression 154
analysis is conducted in CSEOF space. As the first step, regression relationship is 155
8
built between the PC time series of the target variable and those of the predictor 156
variable. That is, 157
T (t) = αm(n)Pm (t)m=1
M∑ + ε (n)(t) , n = 1,2,... , (5) 158
where αm(n){ } are the regression coefficients, ε (n)(t) is the regression error time 159
series for the n th target PC time series, and M is the number of predictor PC 160
time series used for regression. In this study, M = 30 was used; this value was 161
chosen to keep the regression error variance less than 5% for each of the first 20 162
CSEOF modes. The second step of the procedure is written as 163
Dn (r,t) = αm(n)Cm (r,t)m=1
M∑ , n = 1,2,... , (6) 164
where Dn (r,t){ } are regressed loading vectors for the predictor variable. As a 165
result of regression analysis in CSEOF space, the predictor variable can be 166
written as (Seo and Kim 2003; Yeo and Kim 2014) 167
P(r,t) = Dn (r,t)Tn (t)n∑ . (7) 168
Then the evolution of the target variable, Bn (r,t) , and that of the predictor 169
variable, Dn (r,t) , share identical PC (amplitude) time series and are said to be 170
physically consistent. 171
172
3.3. Statistical Downscaling 173
After the regression analysis in CSEOF space, the target and predictor 174
variables are written as 175
T (r,t),P(r,t){ } = Bn (r,t),Dn (r,t){ }Tn (t)n∑ , t ∈D , (8) 176
9
where Bn (r,t),Dn (r,t){ } are essentially the mapping function between the target 177
and the predictor variables. The accuracy of this mapping function depends on 178
the R2 value of regression in (5). If we have a longer predictor variable, then we 179
can write 180
P(r,t) = Dn (r,t) !Tn (t)n∑ , t ∈D + R , (9) 181
where R is the extended period of time. The tilde symbol signifies that the PC 182
time series are estimates from the predictor variable not the target variable. 183
Then, the target variable can be extended by using the estimated PC time series 184
!Tn (t) , i.e., 185
!T (r,t) = Bn (r,t) !Tn (t)n∑ , t ∈D + R . (10) 186
Again, the tilde symbol implies that !T (r,t) is an estimate by using the PC time 187
series derived from the predictor variable. 188
The procedure described in (8)-‐(10) can be used for statistical 189
downscaling. If P(r,t) denotes a dataset with a coarse resolution and T (r,t) 190
represents a dataset with a high resolution, then coarse-‐resolution data can be 191
translated into high-‐resolution data by using (8)-‐(10). The physical relationship 192
between the two datasets in (8) can be determined by using the data over the 193
training period D . Then, high-‐resolution data in the prediction period R can be 194
found from the predictor variable by using (9) and (10). The accuracy of 195
downscaling, of course, depends on how accurate the estimated PC time series 196
are, which, in turn, depends on the accuracy of physical relationship in (8). 197
198
3.4. Verification Method 199
10
To validate the new downscaling approach, the jackknife method is used. 200
From the target data, one year in the data record D is removed and is designated 201
as the prediction year R . Then, physical relationship between the target and 202
predictor variables, (8), is established by using the data in D − R . Then, the 203
target variable is constructed in R by using the downscaling method, (9) and 204
(10). This procedure is repeated for every year in the data record D . The 205
resulting downscaled data !T (r,t) , then, are compared with the raw data T (r,t) 206
by measuring correlation and relative root-‐mean-‐square error (RMSE) defined 207
respectively by 208
ρ =′T (r,t) ! ′T (r,t)
t∑′T (r,t)( )2
t∑ ′!T (r,t)( )2t∑, (11) 209
and 210
RMSE = ′T (r,t)− ! ′T (r,t)( )2t∑ ′T (r,t)( )2
t∑ , (12) 211
where the prime denotes that mean is removed from the time series. 212
213
4. Results 214
4.1. Comparison of the KMA and Reanalysis Winter Temperatures 215
South Korea shows an intricate temperature distribution in winter 216
although it has a small territory. Reanalysis data at their current resolutions 217
cannot faithfully depict the detailed characteristics of winter temperatures. 218
Figure 2 shows the mean and variance of winter surface temperatures from the 219
NCEP/NCAR reanalysis data and those derived from the 60 KMA stations. With 220
this resolution, NCEP/NCAR dataset has only 4 grid points over the South Korean 221
11
peninsula. As can be seen in the figure, the NCEP/NCAR dataset are not capable 222
of depicting the detailed features of winter temperatures in Korea such as the 223
lower mean temperature and stronger temperature variability in the 224
mountainous interior regions, although it captures the general meridional 225
structure of the mean and variance. Without the seasonal cycle, the spatial 226
pattern of variance remains to be similar although the magnitude decreases 227
significantly. Other variables including the NCEP/NCAR lower tropospheric 228
temperatures and the ECMWF surface and lower tropospheric temperatures 229
show similar patterns of mean and variance to those of NCEP/NCAR surface 230
temperature. 231
Figure 3 shows the mean bias, relative RMSE, and correlation of the 232
NCEP/NCAR surface temperatures in comparison with the KMA temperatures. 233
These maps were produced from the difference in temperatures between each of 234
the 60 KMA stations and the closest NCEP/NCAR grid point. The mean bias is, in 235
general, fairly high except for a few stations in the mid-‐western and the southern 236
part of the peninsula; mean bias generally exceeds 2K over much of the 237
peninsula with particularly strong bias on the mountainous eastern side of the 238
peninsula (Fig. 3a). The relative RMSE is also high (> 0.6) on the eastern and 239
southern part of the Korean Peninsula. This means that the standard deviation 240
of the difference between the KMA temperature and NCEP/NCAR temperature is 241
greater than 60% of the standard deviation of the KMA temperature. Correlation 242
between the KMA and NCEP/NCAR temperature is high in the western part of 243
the peninsula but is lower between the western and eastern coasts. Reasonably 244
high correlations over the Korean peninsula indicate that the long-‐term 245
variability in the NCEP/NCAR surface temperature is similar to that in the KMA 246
12
temperature. Figure 3 implies that a statistical downscaling method may be 247
useful if it can alleviate regional differences between the reanalysis and KMA 248
temperatures as depicted in the figure. Without the seasonal cycle, the mean 249
bias is nearly zero since the bias is primarily in the seasonal cycle. Correlation is 250
slightly degraded and RMSE is increased slightly as should be expected. 251
Figure 4 shows the winter temperatures at the four KMA stations (red 252
dots) in Fig. 1 and at the nearest grid points of the NCEP/NCAR surface dataset. 253
For easier comparison, time series are plotted from year 2000. It appears that 254
the NCEP/NCAR temperatures are reasonably similar to the KMA data with an 255
average correlation of 0.85 (0.87, 0.81) at the surface (1000 hPa, 850 hPa) level. 256
While correlations are fairly reasonable, the NCEP/NCAR reanalysis products fall 257
short of the reality in terms of their ability to reproduce the spatial peculiarity in 258
the KMA measurements. Similarly, the ECMWF reanalysis temperature exhibits 259
an average correlation of 0.85 (0.89, 0.79) at the surface (1000 hPa, 850 hPa) 260
level. 261
262
4.2. Test Results 263
By using the Jackknife method, the first 20 CSEOF PC time series were 264
generated as shown in Fig. 5; the first 20 CSEOF modes explain about 90% of the 265
total variability of winter temperatures measured at 60 KMA stations. The black 266
curve in each panel represents the estimated PC time series from the predictor 267
variable, which is the NCEP/NCAR surface temperature. Except for the mode 20, 268
correlations between the PC time series of the KMA data and those estimated 269
from the NCEP/NCAR data are fairly high ( ρ ≥ 0.59 ). Table 1 provides 270
correlations for the first 10 PC time series of all predictor variables tested in this 271
13
study. Since the performance of the downscaling method is similar for all six 272
variables tested here, the results based on the NCEP surface temperatures will be 273
shown below. 274
Figure 6 shows the downscaled temperatures based on the 20 PC time 275
series estimated from the NCEP/NCAR surface data against the 20-‐mode 276
reconstruction of the KMA temperatures at the four stations closest to the 4 277
NCEP/NCAR grid points. Although the downscaled temperatures occasionally 278
underestimate the peaks in the KMA reconstruction data, evolution of the 279
wintertime temperatures in the 35-‐year KMA record are reasonably captured by 280
the developed downscaling method. Correlation between the 20-‐mode 281
reconstruction of the KMA data and the downscaled temperatures based on the 282
NCEP/NCAR surface data are close to 0.93 at all four stations. A comparison of 283
the downscaled temperature and the raw KMA data is shown in Fig. 7. 284
Correlations decrease slightly from those in Fig. 6, since the first 20 modes 285
explain only about 90% of the total variability of the KMA data; this decrease is 286
obviously due to the neglect of the remaining variability in the KMA data. 287
Nonetheless, downscaled temperatures are quite comparable in accuracy to the 288
original reanalysis surface temperatures. 289
Correlations of the 20-‐mode and 10-‐mode downscaled temperatures from 290
the NCEP/NCAR surface data with the original KMA data are shown in Table 2. 291
Correlations are calculated with and without the seasonal cycle at the four 292
stations. The averaged correlation between the 20-‐mode (10-‐mode) downscaled 293
temperature and the KMA temperature is ~0.88 (~0.82) with the seasonal cycle 294
and is ~0.82 (~0.73) without the seasonal cycle. Correlation, of course, 295
decreases slightly by removing the seasonal cycle, which is a major component of 296
14
variability in the data. Correlations of the 20-‐mode (10-‐mode) downscaled 297
temperature with the 20-‐mode (10-‐mode) KMA reconstruction temperature is 298
~0.93 (~0.97) with the seasonal cycle and is ~0.89 (~0.95) without the seasonal 299
cycle. Correlation increases by using the same number of modes for the KMA 300
temperatures. 301
Figure 8 shows difference between the downscaled temperature and the 302
raw KMA temperature together with the difference between the reanalysis and 303
KMA temperatures. Downscaling reduces the mean bias in the reanalysis surface 304
temperatures. The mean bias ranges from 0.93K at Uljin station to 1.93K at 305
Suncheon station in the NCEP/NCAR surface temperatures, which was reduced 306
to ~0.008-‐0.04K after downscaling. The variance of error time series is reduced 307
at two stations (Suncheon and Icheon) but is slightly increased at the other 308
stations. Of course, the purpose of downscaling is to reproduce temperatures 309
accurately away from the reanalysis grid points. 310
Figure 9 summarizes the accuracy of the downscaled temperatures 311
against the raw KMA temperatures. In the presence of the seasonal cycle, 312
correlation is greater than 0.87 all over the peninsula and the relative RMSE is 313
less than ~50%. Even in the absence of the seasonal cycle, correlation is 314
reasonably high (> 0.80) and the relative RMSE is less than ~62%. It should be 315
noted that both correlation and RMSE values are fairly uniform over the 316
peninsula. A comparison between Figs. 8 and 9 reveals that specific regional 317
characteristics of the KMA temperature have been reasonably reproduced by the 318
downscaling method. Tables 3 and 4 show the range of RMSE and correlation 319
values for different datasets. As can be seen in the table, the performance of the 320
developed downscaling method is not overly sensitive to the choice of a 321
15
predictor variable. For six different variables, the range of relative RMSE is 322
(0.462, 0.551) and that of correlation is (0.841, 0.900) at the 60 KMA stations. 323
Figure 10 shows the mean and standard deviation of the raw KMA 324
temperature over the peninsula and the 20-‐mode downscaled temperature 325
based on the NCEP/NCAR surface data. The patterns of the standard deviation 326
are similar between the two although the downscaled temperature 327
underestimates the standard deviation by ~10-‐20%. It is clear that the 328
statistical downscaling method cannot reproduce all the variability in the KMA 329
winter temperatures. Nonetheless, the details of the distribution of temperature 330
variability over the peninsula are faithfully captured by the downscaling method. 331
The patterns of the mean are nearly identical; the mean bias in the reanalysis 332
data has been removed almost completely. 333
334
4.3. Implications of the Test Results 335
General circulation models (GCMs) are frequently used for seasonal 336
predictions. GCMs at present resolutions, however, have limitations in rendering 337
small-‐scale climate variability. The utility of GCM seasonal predictions can be 338
enhanced by using the statistical downscaling method developed in the present 339
study. For example, Fig. 11 shows the regressed PC time series over the 5-‐year 340
prediction interval (2009/2010-‐2013/2014) based on the NCEP/NCAR and 341
ECMWF surface temperatures over the training period (1979/1980-‐2008/2009). 342
This is a stringent test, since daily winter temperatures are predicted for 5 343
consecutive years based on 30-‐year training data. As can be seen in the figure, 344
the amplitudes of the first 10 modes were reasonably predicted with some 345
underestimation for modes 6 and 8. Figure 12 shows the correlation map of 346
16
daily and monthly winter temperatures predicted over the peninsula. It is clear 347
that the predicted temperatures reflect both regional accuracy and details. 348
An added advantage of the CSEOF-‐based downscaling method here is that 349
regional patterns of other variables can also be obtained by carrying out 350
regression analysis in CSEOF space. Upon regression of two KMA variables in 351
CSEOF space, we have 352
T (r,t),S(r,t){ } = Bn (r,t),An (r,t){ }Tn (t)n∑ , (13) 353
where Bn (r,t),An (r,t){ } are two matching evolutions in two different variables 354
T (r,t),S(r,t){ } . By estimating the PC time series of T (r,t) (target variable: KMA 355
temperature) from a predictor variable (e.g., NCEP/NCAR surface temperature), 356
we can also generate the detailed spatial pattern of other KMA variables based 357
on (13). Of course, the accuracy of the regression procedure depends on the 358
accuracy of regression between two KMA variables. Nonetheless, this idea is 359
intriguing considering the reasonable performance of the developed 360
downscaling method as applied to surface temperatures. 361
362
5. Summary and Conclusions 363
A statistical downscaling method based on CSEOFs was developed in this 364
study. The resulting downscaling method was tested in the construction of 365
winter temperatures at 60 KMA stations over South Korea by using the 366
NCEP/NCAR and ECMWF reanalysis datasets. The essence of the technique is to 367
identify mapping relationships (matching evolutions) in CSEOF space between a 368
target variable (KMA temperatures) and a predictor variable (NCEP/NCAR or 369
ECMWF winter temperatures). Then, the evolutions in a predictor variable are 370
17
translated into matching evolutions in a target variable. This strategy should 371
work if a predictor variable is reasonably accurate in depicting long-‐term 372
evolution in a target variable. 373
In order to validate the downscaling method, winter temperatures at the 374
60 KMA stations were constructed by using the jackknife method. The 375
performance of the downscaling method was assessed in terms of mean bias, 376
relative RMSE, and correlation at each station. The downscaled temperatures 377
improve the reanalysis temperatures, and exhibit little mean bias, smaller 378
relative RMSE, and higher correlation at most KMA stations. The downscaling 379
method reproduces the regional characteristics of temperature in a faithful 380
manner and is little sensitive to the choice of a predictor variable tested in this 381
study. In practice, of course, the accuracy of downscaling depends not only on 382
the method but also on the predictor field itself. 383
In the present resolutions, the utility of GCM predictions is very limited. 384
As demonstrated in Figs. 11 and 12, GCM predictions can be enhanced in terms 385
of systematic bias and spatial details by using the developed statistical 386
downscaling method. It should be noted that the temporal resolutions of GCM 387
predictions could also be improved by using the CSEOF-‐based downscaling 388
method. This can be accomplished by reproducing the PC time series of 389
temporally dense target variable (say, daily observations) from PC time series of 390
temporally coarse predictor variables (say, monthly GCM outputs). 391
392
Acknowledgments: This work was supported by SNU-‐Yonsei Research 393
Cooperation Program through Seoul National University (SNU) in 2014. 394
18
References 395
Christensen, J. H., B. Machenhauer, R. G. Jones, C. Schar, P. M. Ruti, M. Castro, and 396
G. Visconti, 1997: Validation of present-day regional climate simulations over 397
Europe: LAM simulations with observed boundary conditions. Clim. Dyn., 13, 398
489–506. 399
Coulibaly, P., Y. B. Dibike, and F. Anctil, 2005: Downscaling precipitation and 400
temperature with temporal neural networks. J. Hydrometeor., 6, 483–496. 401
Cox, P., R. Betts, C. Bunton, R. Essery, P. R. Rowntree, and J. Smith, 1999: The 402
impact of new land-‐surface physics on the GCM simulation and climate 403
sensitivity. Clim. Dyn., 15, 183-‐203. 404
Dee, D. P., and Coauthors, 2011: The ERA-‐Interim reanalysis: configuration and 405
performance of the data assimilation system. Q. J. Meteorol. Soc., 137, 553-‐406
597. 407
Feddersen, H., and U. Andersen, 2005: A method for statistical downscaling of 408
seasonal ensemble predictions. Tellus, Ser. A, 57, 398– 408. 409
Fennessy, M. J., and J. Shukla, 2000: Seasonal prediction over North America with 410
a regional model nested in a global model. J. Clim., 13, 2605–2627. 411
Fuentes, U., and D. Heimann, 2000: An improved statistical-‐dynamical 412
downscaling scheme and its application to the Alpine precipitation 413
climatology. Theor. Appl. Climatol., 65, 119– 135. 414
Giorgi, F., 1990: Simulation of regional climate using a limited area model nested 415
in a general-‐circulation model. J. Clim., 3, 941– 963. 416
Hansen, J., I. Fung, A. Lacis, D. Rind, S. Lebedeff, R. Ruedy, G. Russell, P. Stone, 417
1988: Global climate changes as forecast by Goddard Institute for Space 418
Studies three-‐dimensional model. J. Geophys. Res., 93, 9341-‐9364. 419
19
Hewitson, B. C., and R. G. Crane, 1996: Climate downscaling: Techniques and 420
application. Clim. Res., 7, 85– 95. 421
Hoskins, B. J., 2013: The potential for skill across the range of the seamless 422
weather-‐climate prediction problem: A stimulus for our science. Q. J. Roy. 423
Meteor. Soc., 139, 573–584, doi:10.1002/qj.1991. 424
Huth, R., 2002: Statistical downscaling of daily temperature in central Europe. J. 425
Clim., 15, 1731–1742. 426
Huth, R., and J. Kysely, 2000: Constructing site-‐specific climate change scenarios 427
on a monthly scale using statistical downscaling. Theor. Appl. Climatol., 66, 428
13–27. 429
IPCC, 1996: Climate Change 1995: The Science of Climate Change [Houghton, J. T., 430
et al. (eds.)]. Cambridge University Press, Cambridge, United Kingdom and 431
New York, NY, USA, 236-‐237 pp. 432
IPCC, 2007: Climate Change 2007: The Physical Science Basis [Solomon, S., et al. 433
(eds.)]. Cambridge University Press, Cambridge, United Kingdom and New 434
York, NY, USA, 602-‐603 pp. 435
IPCC, 2013: Working Group I Contribution to the IPCC Fifth Assessment Report 436
(AR5), Climate Change 2013: The Physical Science Basis. 437
Intergovernmental Panel on Climate Change, Geneva, Switzerland. 438
Ji, Y., and A. D. Vernekar, 1997: Simulation of the Asian summer monsoons of 439
1987 and 1988 with a regional model nested in a global GCM. J. Clim., 10, 440
1965–1979. 441
Jones, R. G., J. M. Murphy, and M. Noguer, 1995: Simulation of climate change over 442
Europe using a nested regional climate model. Part I. Assessment of 443
20
control climate including sensitivity to location of lateral boundaries. Q. J. 444
Roy. Meteor. Soc., 121, 1413-‐1449. 445
Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-‐Year Reanalysis Project. 446
Bull. Amer. Meteor. Soc., 77, 437-‐471. 447
Kim, K.-‐Y., and G. R. North, 1997: EOFs of harmonizable cyclostationary 448
processes. J. Atmos. Sci., 54, 2416–2427. 449
Kim, K.-‐Y., and Q. Wu, 1999: A comparison study of EOF techniques: Analysis of 450
nonstationary data with periodic statistics. J. Clim., 12, 185-‐199. 451
Kim, K.-‐Y., G. R. North, and J. Huang, 1996: EOFs of one-‐dimensional 452
cyclostationary time series: Computations, examples, and stochastic 453
modeling. J. Atmos. Sci., 53, 1007–1017. 454
Kimoto, M., N. Yasutomi, C. Yokoyama, and S. Emori, 2005: Projected changes in 455
precipitation characteristics near Japan under the global warming. 456
Scientific online Letters on the Atmosphere, 1, 85-‐88, 457
doi:10.2151/sola.2005-‐023. 458
Lim, Y.-‐K., D. W. Shin, S. Cocke, T. E. LaRow, J. T. Schoof, J. J. O’Brien, and E. P. 459
Chassignet, 2007: Dynamically and statistically downscaled seasonal 460
simulations of maximum surface air temperature over the southeastern 461
United States. J. Geophys. Res., 112, D24102, doi:10.1029/2007JD008764. 462
Marchesiello, P., J. C. McWilliams, and A. Shchepetkin, 2001: Open boundary 463
conditions for long-‐term integration of regional oceanic models. Ocean 464
Model., 3, 1–20. 465
Misra, V., P. A. Dirmeyer, and B. P. Kirtman, 2003: Dynamical downscaling of 466
seasonal simulations over South America. J. Clim., 16, 103– 117. 467
Murphy, J. M., D. M. H. Sexton, D. N. Barnett, G. S. Jones, M. J. Webb, M. Collins, and 468
21
D. A. Stainforth, 2004: Quantification of modelling uncertainties in a large 469
ensemble of climate change simulations. Nature, 430, 768–772. 470
Palmer, T. N., F. J. Doblas-Reyes, A. Weisheimer, and M. J. Rodwell, 2008: Toward 471
Seamless Prediction: Calibration of Climate Change Projections Using 472
Seasonal Forecasts. Bull. Amer. Meteor. Soc., 89, 459–470. 473
Robertson, A. W., S. Kirshner, and P. Smyth, 2004: Downscaling of daily rainfall 474
occurrence over northeast Brazil using a hidden Markov model. J. Clim., 475
17, 4407– 4424. 476
Sakamoto, T. T., et al, 2004: Far-‐reaching effects of Hawaiian Islands in the 477
CCSR/NIES/FRCGC high-‐resolution climate model. Geophys. Res. Lett., 31, 478
doi:10.1029/2004GL020907. 479
Seo, K.-‐H., and K.-‐Y. Kim, 2003: Propagation and initiation mechanisms of the 480
Madden-‐Julian oscillation. J. Geophys. Res.. 108, 4384, 481
doi:10.1029/2002JD002876. 482
Shukla, J., 2009: Seamless prediction of weather and climate: A new paradigm for 483
modeling and prediction research. Climate Test Bed Joint Seminar Series, 484
Camp Springs, MD, NOAA, 8 pp. 485
Sun, L., D. F. Moncunill, H. Li, A. D. Moura, F. D. A. D. S. Filho, and S. E. Zebiak, 2006: 486
An operational dynamical downscaling prediction system for Nordeste 487
Brazil and the 2002–04 real-‐time forecast evaluation. J. Clim., 19, 1990– 488
2007. 489
Widmann, M., C. S. Bretherton, and E. P. Salathe Jr., 2003: Statistical precipitation 490
downscaling over the northwestern United States using numerically 491
simulated precipitation as a predictor. J. Clim., 16, 799– 816. 492
22
Wilby, R. L., and T. M. L. Wigley, 1997: Downscaling general circulation model 493
output: A review of methods and limitations. Prog. Phys. Geogr., 21, 530–494
548. 495
Wilby R. L., S. P. Charles, E. Zorita, B. Timbal, P. Whetton, L. O. Mearns, 2004: 496
Guidelines for use of climate scenarios developed from statistical 497
downscaling methods, Supporting material of the Intergovernmental Panel 498
on Climate Change, available from the DDC of IPCC TGCIA, 27. 499
Wilby, R. L., T. M. L. Wigley, D. Conway, P. D. Jones, B. C. Hewitson, J. Main, and D. 500
S. Wilks, 1998: Statistical downscaling of general circulation model output: 501
A comparison of methods. Water Resour. Res., 34, 2995– 3008. 502
Wilks, D. S., 1999: Multisite downscaling of daily precipitation with a stochastic 503
weather generator. Clim. Res., 11, 125– 136. 504
Yeo, S.-‐R., and K.-‐Y. Kim, 2014: Global warming, low-‐frequency variability, and 505
biennial oscillation: An attempt to understand the physical mechanisms 506
driving major ENSO events. Clim. Dyn., 43, 771-‐786. 507
23
Table Captions 508
Table 1. Correlation between the first 10 PC time series of KMA winter 509
temperature for 35 years and the regressed PC time series of the NCEP/NCAR 510
surface, 1000 and 850 hPa temperatures and those of the ECMWF surface, 1000 511
and 850 hPa temperatures. 512
Table 2. Correlation of the 20-‐mode and 10-‐mode downscaled (d) NCEP/NCAR 513
surface temperature data with the original (o) and reconstructed (r) KMA data. 514
Correlation is calculated in two cases with the seasonal cycle and without the 515
seasonal cycle at four stations closest to the four NCEP/NCAR grid points. 516
Table 3. The lowest three and the highest three RMSE values of the 20-‐mode 517
downscaled NCEP/NCAR and ECMWF temperatures with those at the 60 KMA 518
stations. 519
Table 4. The lowest three and the highest three correlation values of the 20-‐520
mode downscaled NCEP/NCAR and ECMWF temperatures with those at the 60 521
KMA stations. 522
24
Figure Captions 523
Figure 1. The locations of the 60 Korea Meteorological Administration (KMA) 524
stations. The black dotted lines represent the NCEP/NCAR grids for 2 m 525
temperature, the blue dotted lines the NCEP/NCAR grids for temperatures at 526
pressure levels, and the red dotted lines the ERA interim temperatures. The red 527
dots denote the stations closest to the four NCEP/NCAR grid points. 528
Figure 2. The mean and variance of the (left) NCEP surface and (right) KMA raw 529
temperatures: (a) and (b) represent the mean, (c) and (d) the variance, and (e) 530
and (f) the variance without the seasonal cycle. 531
Figure 3. Mean bias (top), relative RMSE (middle), and correlation (bottom) of 532
the NCEP/NCAR surface temperature against the KMA temperatures. At each of 533
the 60 KMA stations, the closest NCEP/NCAR grid point is taken to calculate 534
these statistics. 535
Figure 4. The KMA temperature (blue) and the raw NCEP/NCAR surface 536
temperature (red) at the four KMA stations closest to the NCEP grid points (red 537
dots in Fig. 1). 538
Figure 5a. Comparison of the CSEOF PC time series (modes 1-‐10) of (red) the 539
KMA winter temperature for 1979/1980-‐2013/2014, and (black) the PC time 540
series generated from the NCEP surface temperature based on the Jackknife 541
method. 542
Figure 5b. Same as Fig. 5a, but for modes 11-‐20. 543
Figure 6. Comparison of (red) the 20-‐mode downscaled NCEP surface 544
temperature and (blue) the 20-‐mode reconstruction of the KMA temperature at 545
the four stations closest to the NCEP grids. 546
25
Figure 7. Comparison of (red) the 20-‐mode downscaled NCEP surface 547
temperature and (blue) the raw KMA temperature at the four stations closest to 548
the NCEP grids. 549
Figure 8. Error time series (blue) between the raw KMA temperature and the 550
20-‐mode downscaled temperature in Fig. 6 and (red) the raw KMA temperature 551
and the NCEP surface temperature at the four KMA stations in Fig. 1 (red dots). 552
Figure 9. Correlation and RMSE of the downscaled temperature from the NCEP 553
surface data and the raw KMA temperature: with the seasonal cycle in (a) and 554
(b), and without the seasonal cycle in (c) and (d). 555
Figure 10. Standard deviation (upper panels) and mean (lower panels) of the 556
raw KMA temperature (left column) and the 20-‐mode downscaled temperature 557
from the NCEP surface data (right column). 558
Figure 11. The first 10 PC time series of (red) the KMA winter temperature 559
(1979/1980 -‐ 2013/2014) and the regressed PC time series from (red) the 560
NCEP/NCAR and (blue) ECMWF surface temperature. Regression relationship is 561
determined based on the data in the training period (1979/1980-‐2008/2009) 562
and the time series from 2009/2010-‐2013/2014 are prediction based on the 563
regressed PC time series. 564
Figure 12. Correlation (left column) and the relative RMSE (right column) 565
between the 20-‐mode downscaled NCEP/NCAR surface temperature and the raw 566
KMA temperature for the prediction period (2009/2010-‐2013/2014): (a) and 567
(b) are for the daily temperature, and (c) and (d) are for the monthly 568
temperature. 569
26
Table 1. Correlation between the first 10 PC time series of KMA winter 570 temperature for 35 years and the regressed PC time series of the NCEP/NCAR 571 surface, 1000 and 850 hPa temperatures and those of the ECMWF surface, 1000 572 and 850 hPa temperatures. The first 10 modes explain ~73% and the first 20 573 modes explain ~90% of the total variability of the KMA temperatures. 574 575
Data Mode
NCEP ECMWF
Surface 1000 hPa 850 hPa Surface 1000 hPa 850 hPa
1st (34.8%) 0.995 0.991 0.981 0.995 0.993 0.979
2nd (8.3%) 0.975 0.964 0.958 0.985 0.981 0.963
3rd (5.2%) 0.953 0.965 0.962 0.942 0.968 0.949
4th (4.6%) 0.969 0.967 0.951 0.972 0.977 0.954
5th (4.2%) 0.971 0.958 0.957 0.962 0.964 0.953
6th (3.7%) 0.966 0.963 0.950 0.968 0.966 0.944
7th (3.6%) 0.969 0.969 0.971 0.973 0.976 0.971
8th (3.0%) 0.931 0.936 0.871 0.961 0.954 0.905
9th (2.8%) 0.933 0.911 0.895 0.922 0.921 0.869
10th (2.5%) 0.936 0.918 0.887 0.926 0.932 0.891
576
27
Table 2. Correlation of the 20-‐mode and 10-‐mode downscaled (d) NCEP/NCAR 577 surface temperature data with the original (o) and reconstructed (r) KMA data. 578 Correlation is calculated in two cases with the seasonal cycle and without the 579 seasonal cycle at four stations closest to the four NCEP/NCAR grid points. 580 581
20-‐mode With the seasonal cycle Without the seasonal cycle
Corr (o,d) Corr (r,d) Corr (o,d) Corr (r,d)
Suncheon 0.880 0.935 0.815 0.898 Busan 0.880 0.928 0.834 0.897 Icheon 0.883 0.935 0.806 0.889 Uljin 0.871 0.926 0.817 0.892
10-‐mode With the seasonal cycle Without the seasonal cycle
Corr (o,d) Corr (r,d) Corr (o,d) Corr (r,d)
Suncheon 0.834 0.971 0.732 0.950 Busan 0.820 0.968 0.739 0.950 Icheon 0.841 0.971 0.726 0.946 Uljin 0.814 0.967 0.725 0.949
582
28
Table 3. The lowest three and the highest three RMSE values of the 20-‐mode 583 downscaled NCEP/NCAR and ECMWF temperatures with those at the 60 KMA 584 stations. 585 586
Data Station
NCEP/NCAR ECMWF
Surface 1000 hPa 850 hPa Surface 1000 hPa 850 hPa
1st 0.474 0.479 0.505 0.466 0.462 0.501
2nd 0.474 0.480 0.506 0.468 0.465 0.501
3rd 0.474 0.480 0.507 0.469 0.465 0.502
58th 0.514 0.521 0.549 0.515 0.508 0.542
59th 0.516 0.525 0.551 0.516 0.508 0.544
60th 0.517 0.527 0.551 0.523 0.517 0.544 587
29
Table 4. The lowest three and the highest three correlation values of the 20-‐588 mode downscaled NCEP/NCAR and ECMWF temperatures with those at the 60 589 KMA stations. 590 591
Data Station
NCEP/NCAR ECMWF
Surface 1000 hPa 850 hPa Surface 1000 hPa 850 hPa
1st 0.891 0.887 0.871 0.894 0.900 0.872
2nd 0.890 0.886 0.870 0.893 0.900 0.872
3rd 0.890 0.885 0.869 0.892 0.900 0.871
58th 0.869 0.864 0.842 0.869 0.873 0.847
59th 0.867 0.860 0.841 0.867 0.873 0.844
60th 0.867 0.860 0.841 0.862 0.866 0.844 592
30
593 Figure 1. The locations of the 60 Korea Meteorological Administration (KMA) 594 stations. The black dotted lines represent the NCEP/NCAR grids for 2 m 595 temperature, and the red dotted lines the ERA interim temperatures. The red 596 dots denote the stations closest to the four NCEP/NCAR grid points. 597
31
598 599
600 601
602 603
Figure 2. The mean and variance of the (left) NCEP/NCAR surface and (right) 604 KMA raw temperatures: (a) and (b) represent the mean, (c) and (d) the variance, 605 and (e) and (f) the variance without the seasonal cycle. 606
32
607
608
609 610 Figure 3. Mean bias (top), relative RMSE (middle), and correlation (bottom) of 611 the NCEP/NCAR surface temperature against the KMA temperatures: (left) with 612 the seasonal cycle, and (right) without the seasonal cycle. At each of the 60 KMA 613 stations, the closest NCEP/NCAR grid point is taken to calculate these statistics. 614
33
615 616 Figure 4. The KMA temperature (blue) and the raw NCEP/NCAR surface 617 temperature (red) at the four KMA stations closest to the NCEP grid points (red 618 dots in Fig. 1). Time series are plotted from year 2000 for easier comparison. 619
corr (kma,NCEP surf) = 0.814
corr (kma,NCEP surf) = 0.900
corr (kma,NCEP surf) = 0.814
corr (kma,NCEP surf) = 0.875
34
620 621 Figure 5a. Comparison of the CSEOF PC time series (modes 1-‐10) of (red) the 622 KMA winter temperature for 1979/1980-‐2013/2014, and (black) the PC time 623 series generated from the NCEP surface temperature based on the Jackknife 624 method. 625
0
2
4
-2
0
2
-2
0
2
-2
0
2
-2
0
2
4
-2
0
2
-2
0
2
-2
0
2
-2
0
2
-2
0
2
1980 1985 1990 1995 2000 2005 2010
35
626 627 Figure 5b. Same as Fig. 5a, but for modes 11-‐20. 628
-2
0
2
-2
0
2
-2
0
2
-2
0
2
-2
0
2
-2
0
2
0
2
-2
0
2
0
-2
0
2
1980 1985 1990 1995 2000 2005 2010
36
629 630 Figure 6. Comparison of (red) the 20-‐mode downscaled NCEP surface 631 temperature and (blue) the 20-‐mode reconstruction of the KMA temperature at 632 the four stations closest to the NCEP grids. 633
corr (recon,downscaled) = 0.935
corr (recon,downscaled) = 0.928
corr (recon,downscaled) = 0.935
corr (recon,downscaled) = 0.926
37
634 635 Figure 7. Comparison of (red) the 20-‐mode downscaled NCEP surface 636 temperature and (blue) the raw KMA temperature at the four stations closest to 637 the NCEP grids. 638
corr (KMA,downscaled) = 0.880
corr (KMA,downscaled) = 0.880
corr (KMA,downscaled) = 0.883
corr (KMA,downscaled) = 0.871
38
639 640 Figure 8. Error time series (blue) between the raw KMA temperature and the 641 20-‐mode downscaled temperature in Fig. 6 and (red) the raw KMA temperature 642 and the NCEP surface temperature at the four KMA stations in Fig. 1 (red dots). 643
39
644 645
646 647 Figure 9. Correlation and RMSE of the downscaled temperature from the NCEP 648 surface data and the raw KMA temperature: with the seasonal cycle in (a) and 649 (b), and without the seasonal cycle in (c) and (d). 650
40
651
652 653 Figure 10. Standard deviation (upper panels) and mean (lower panels) of the 654 raw KMA temperature (left column) and the 20-‐mode downscaled temperature 655 from the NCEP surface data (right column). 656
41
657 658
Figure 11. The first 10 PC time series of (red) the KMA winter temperature 659 (1979/1980 -‐ 2013/2014) and the regressed PC time series from (red) the 660 NCEP/NCAR and (blue) ECMWF surface temperature. Regression relationship is 661 determined based on the data in the training period (1979/1980-‐2008/2009) 662 and the time series from 2009/2010-‐2013/2014 are prediction based on the 663 regressed PC time series. 664
42
665 666
667 668
Figure 12. Correlation (left column) and the relative RMSE (right column) 669 between the 20-‐mode downscaled NCEP/NCAR surface temperature and the raw 670 KMA temperature for the prediction period (2009/2010-‐2013/2014): (a) and 671 (b) are for the daily temperature, and (c) and (d) are for the monthly 672 temperature. 673
