Improving Statistical Downscaling of General Circulation Models

Figures & data

Fig. 1 Grid boxes from a general circulation model (CGCM3) with horizontal resolution of about 300 km by 400 km are plotted over Atlantic Canada. Observations used in this study were taken at Shearwater Airport, Nova Scotia, Canada (44.63°N, 63.5°W). Shearwater Airport (red dot) is about 4 km east of the downtown core of Halifax, Nova Scotia, Canada.

Fig. 2 The black line in (a) represents observed T _min (degrees Celsius) from Shearwater Airport, Nova Scotia, for a 5-year period, 1961–65. The red line in (a) represents the fitted seasonal cycle (fitted over the historical period 1961–2000). Time series in (b) represents the daily anomaly constructed by subtracting the red line from the black line in (a). Time series in (c) and (d) are analogous to (a) and (b) except they are for T _max.

Table 1. Regression coefficients for the seasonal cycles of observed T _min and T _max at Shearwater, Nova Scotia, in units of degrees Celsius.

Variable	T min	T max
μ	3.07	10.82
α 1	−9.47	−10.12
β 1	−5.79	−5.65
α 2	−0.49	−0.09
β 2	0.06	0.18
α 3	−0.21	−0.02
β 3	−0.72	−0.23

Table 2. Original names (set of 25) of NCEP and CGCM3 predictors. The subsets for each season chosen through the predictor selection process are also shown by the checkmark. Winds in the table are geostrophic winds.

Number	Original	Winter	Summer
1	Mean sea level pressure	✓	✓
2	1000 hPa wind speed	✓	✓
3	1000 hPa zonal wind	✓	✓
4	1000 hPa meridional wind	✓
5	1000 hPa vorticity		✓
6	1000 hPa wind direction
7	1000 hPa divergence
8	500 hPa wind speed	✓	✓
9	500 hPa zonal wind	✓	✓
10	500 hPa meridional wind	✓	✓
11	500 hPa vorticity	✓	✓
12	500 hPa wind direction
13	500 hPa divergence
14	500 hPa geopotential height	✓
15	850 hPa wind speed	✓	✓
16	850 hPa zonal wind	✓	✓
17	850 hPa meridional wind	✓	✓
18	850 hPa vorticity	✓	✓
19	850 hPa wind direction
20	850 hPa divergence
21	850 hPa geopotential height	✓	✓
22	500 hPa specific humidity		✓
23	850 hPa specific humidity	✓	✓
24	1000 hPa specific humidity	✓
25	Surface mean temperature	✓

Fig. 3 (a) Time series of the geopotential height (blue) at 500 hPa produced by the CGCM3 at the model grid box containing Shearwater, Nova Scotia, during the period 2001–70. The vertical red dotted lines divide the future period into three separate future periods: 2001–10, 2011–40 and 2041–70. The black line in (a) represents the linear trend (with the mean) in each future period. The seasonal cycle fitted to each future period (red, green, magenta) detrended data (geopotential height (blue) minus trend (black)) is also shown in (a). Time series in (b) are daily anomalies constructed by taking the geopotential height minus the trend in each period and finally subtracting the seasonal cycle in each future period. Panel (b) also shows the seasonal cycle mean which was added for each period as the final step.

Fig. 4 Distributions of T _mean in (a) winter and (b) summer generated from NCEP (black) and CGCM3 (red) datasets between 1961 and 2000 at Shearwater, Nova Scotia. Both the NCEP and CGCM3 predictors are Z-scores. The distribution is created by binning the data in bins 0.5 of a Z-score wide. The probability is calculated by taking the number of measurements occurring in each bin and dividing by the total number of measurements.

Table 3. The numbers in the percent (%) column refer to the fraction of total variance explained in the original dataset by each of the seventeen principal components (PCs) for winter. Here R refers to the correlation coefficient of each PC with T _min and T _max, and γ refers to the regression coefficient, in units of degrees Celsius, of those PCs used in the winter regression.

PC	%	T min		T max
		R	γ	R	γ
1	29.43	−0.30	−0.76	−0.41	−0.93
2	24.03	0.03	—	−0.22	−0.56
3	19.94	0.52	1.64	0.51	1.43
4	9.08	0.34	1.63	0.32	1.33
5	5.89	0.17	1.07	0.16	0.82
6	3.53	−0.27	−2.00	−0.30	−2.08
7	2.70	−0.28	−2.44	−0.26	−1.99
8	2.05	−0.09	—	−0.03	—
9	1.11	0.11	1.42	0.09	—
10	0.90	−0.29	−4.42	−0.15	−2.04
11	0.51	−0.06	—	−0.06	—
12	0.32	0.09	—	0.08	—
13	0.20	0.02	—	0.03	—
14	0.14	−0.01	—	−0.01	—
15	0.13	−0.02	—	−0.05	—
16	0.02	−0.02	—	−0.05	—
17	0.02	−0.05	—	−0.07	—

Table 4. The numbers in the percent (%) column refer to the fraction of total variance explained in the original dataset by each of the fifteen Principal Components (PCs) for summer. Here R refers to the correlation coefficient of each PC with T _min and T _max, and γ refers to the regression coefficient, in units of degrees Celsius, of those PCs used in the summer regression.

PC	%	T min		T max
		R	γ	R	γ
1	30.97	−0.26	−0.34	−0.16	−0.32
2	20.93	−0.39	−0.64	0.14	0.38
3	17.10	0.06	—	0.28	0.83
4	7.96	0.00	—	0.14	0.72
5	6.96	−0.08	—	−0.16	−0.80
6	5.17	0.35	1.16	0.45	2.32
7	3.42	−0.03	—	0.05	—
8	2.72	−0.14	−0.69	−0.11	−0.84
9	1.56	−0.15	−0.93	0.01	—
10	0.99	0.09	—	0.24	2.98
11	0.87	−0.02	—	−0.09	—
12	0.71	0.03	—	0.06	—
13	0.46	0.11	0.99	0.08	—
14	0.14	0.01	—	−0.05	—
15	0.05	0.34	11.83	0.34	18.67

Table 5. The percentage of total variance explained by the regression for T _min and T _max during the training period (1961–90) and the validation period (1991–2000) for winter and summer.

Season	Training T min	Validation T min	Training T max	Validation T max
Winter	74	76	77	77
Summer	52	53	55	56

Fig. 5 (a) Time series of observed daily anomalies of T _min (degrees Celsius) in winter (black) for two years (1990–91). The NCEP prediction of the daily T _min anomaly in winter for the last year of the training period (1990) is shown in red. The blue line represents the winter T _min NCEP prediction of the daily anomaly for the first year of the validation period (1991). (b) As in (a) except for T _max in winter. Time series in (c) and (d) are the same as in (a) and (b), except for summer.

Fig. 6 Distributions of the observed (black), CGCM3 predicted (red dashed) and raw CGCM3 (blue dashed) total T _min and T _max in winter and summer for the period 1961–2000. To create the distribution the data were separated into bins that were two degrees Celsius wide over the range of the data. The sample probability on the vertical axis refers to the number of measurements occurring within a particular bin divided by the total number of measurements.

Fig. 7 Distribution of CGCM3 predicted total T _max and T _min in winter and summer in the historical period (1961–90) and three future periods (2011–40, 2041–70, 2071–2100). The distributions are created by binning the data in two degree Celsius bins. The sample probability is found by dividing the number of measurements in a particular bin by the total number of measurements.

Table 6. The mean and standard deviation for the predicted future distributions of CGCM3-predicted total T _min in the winter and summer seasons for the three future periods (2011–40, 2041–70, 2071–2100). The change in mean (δ_μ ) from the historical to each future tri-decade is also shown. The historical observed distribution mean and standard deviation are also shown. The units in this table are degrees Celsius.

Period	Season	μ	δμ	σ	Historical μ	Historical σ
2011–40	Winter	−5.33	1.67	5.92
2041–70	Winter	−3.78	3.22	6.00	−7.00	6.10
2071–2100	Winter	−1.42	5.58	5.94
2011–40	Summer	13.31	0.77	3.03
2041–70	Summer	14.12	1.58	3.06	12.54	3.08
2071–2100	Summer	15.29	2.75	3.10

Table 7. The mean and standard deviation for the predicted future distributions of CGCM3-predicted total T _max in the winter and summer seasons for the three future periods (2011–40, 2041–2070, 2071–2100). The change in mean (δ_μ ) from the historical to each future tri-decade is also shown. The historical observed distribution mean and standard deviation are also shown. The units in this table are degrees Celsius.

Period	Season	μ	δμ	σ	Historical μ	Historical σ
2011–40	Winter	1.77	1.13	5.06
2041–70	Winter	2.92	2.28	5.15	0.64	5.48
2071–2100	Winter	4.61	3.97	5.17
2011–40	Summer	22.08	1.11	3.50
2041–70	Summer	23.25	2.28	3.48	20.97	3.99
2071–2100	Summer	24.72	3.75	3.56

Table 8. Values of γ ² for predicting the daily anomalies of T _min and T _max in winter and summer during the historical period (1961–2000) using the SD method with and without removal of the seasonal cycles from predictors and predictands prior to training the regression model. Values of γ ² in predicting T _max with SDSM are also shown.

Cases	T min		T max
	Winter	Summer	Winter	Summer
Seasonal cycles removed	0.25	0.51	0.22	0.45
Seasonal cycles included	0.26	0.71	0.23	0.52
Annual regression	0.30	1.01	0.31	0.82
SDSM	–—	–—	0.78	1.04