Electronic Supplement Material

Reconstructing the development of Baltic Sea eutrophication 1850 - 2006

Gustafsson B.G., Schenk F., Blenckner T., Eilola K., Meier H.E.M., Müller-Karulis B., Neumann T., Ruoho-Airola T., Savchuk O.P., Zorita E.

Figure S1

Map of the Baltic Sea with BALTSEM sub-basins indicated by name and number. Square markers represent the positions of the light vessels from which temperature measurements were used for validation.

Electronic Supplementary Material S2

Validation of meteorological forcing (HiResAFF)

In order to estimate the quality of the meteorological forcing of HiResAFF on a seasonal scale, it is compared to coarsely gridded NCEP/NCAR reanalysis and the high-resolution RCAO/ERA40 simulation. The RCAO/ERA40 formed the basis of the analogous fields that have been used for HiResAFF in the analog-remapping. As measures of skill we estimate the Pearson correlation (cor), the deviation of the mean (bias) and the ratio of variance (, Eq. 1) between all three datasets. The NCEP/NCAR reanalysis is used as reference (ref) for the inter-comparison with the reconstruction or model simulation (rec) HiResAFF and RCAO, whereas RCAO serves as reference relative to HiResAFF. The deviation of the seasonal mean (seasonal sum in case of precipitation) is estimated as the difference of mod minus ref. The ratio of variance is defined as

(1)

Values of <1 indicate an underestimation, values of >1 an overestimation of the reconstructed or modelled variance compared to the reference and=1 reflects an exact reproduction of the variance. All errors in the reconstruction or simulation contribute to the reduction in error (RE, Eq. 2a) relative to ref, formally defined as the loss from a perfect reproduction (RE=1) caused by the root-mean-square-error (RMSE) divided by the standard deviation of the reference

(2a)

Positive values (0 < RE ≤ 1) indicate at least a better skill than the climatological mean of the reference (RE=0) and negative values indicate lower skill. However, as the bias for some variables is usually large for regional climate models like RCAO and hence also HiResAFF (and NCEP/NCAR only provides large-scale information of the variables) we present the unbiased reduction in error (REu, Eq. 2b) in Table 2.1 to estimate whether the meteorological forcing successfully reproduces the year-to-year variability. The unbiased REu is defined according to Eq. 2a replacing the RMSE by the standard error, being the standard deviation of the residuum between reconstruction and reference

(2b)

Table S2.1 Seasonal inter-comparison between the three datasets HiResAFF, NCEP reanalysis and RCAO/ERA40 for the central Baltic Sea (52.5°N – 62.5°N, 17.5°E – 22.5°E) for the period 1961-2007: correlation (cor), mean bias, ratio of variance () and unbiased reduction in error (REu, Eq. 2b). Numbers in italic: non-significant correlation or significant bias (2-sided t-test with p<0.05), significant deviation of variance (2-sided F-test with p<0.10). Bold REu where also biased RE> 0 (Eq. 2a).

SLP
[hPa] / HIRESAFF-NCEP / HIRESAFF-RCAO/ERA40 / RCAO/ERA40-NCEP
cor / bias / / REu / cor / bias / / REu / cor / bias / / REu
DJF / 0.97 / -0.16 / 0.86 / 0.77 / 0.97 / 0.11 / 0.75 / 0.73 / 0.99 / -0.27 / 1.14 / 0.76
MAM / 0.96 / 0.06 / 0.95 / 0.76 / 0.93 / 0.31 / 0.68 / 0.61 / 0.95 / -0.25 / 1.41 / 0.61
JJA / 0.96 / 0.64 / 0.82 / 0.67 / 0.79 / 0.08 / 0.91 / 0.42 / 0.87 / 0.56 / 0.90 / 0.46
SON / 0.99 / 0.31 / 0.64 / 0.65 / 0.92 / 0.25 / 0.57 / 0.58 / 0.93 / 0.07 / 1.12 / 0.61
WIND
[m/s] / HIRESAFF-NCEP / HIRESAFF-RCAO/ERA40 / RCAO/ERA40-NCEP
cor / bias / / REu / cor / bias / / REu / cor / bias / / REu
DJF / 0.90 / 0.74 / 1.21 / 0.52 / 0.89 / -0.18 / 0.88 / 0.55 / 0.95 / 0.93 / 1.37 / 0.63
MAM / 0.67 / 0.34 / 1.25 / 0.13 / 0.69 / -0.21 / 0.76 / 0.25 / 0.71 / 0.54 / 1.63 / 0.10
JJA / 0.68 / 0.56 / 1.43 / 0.10 / 0.62 / -0.13 / 1.42 / 0.02 / 0.71 / 0.69 / 1.01 / 0.24
SON / 0.76 / 0.63 / 1.18 / 0.27 / 0.77 / -0.25 / 0.79 / 0.35 / 0.92 / 0.88 / 1.50 / 0.49
T2M
[K] / HIRESAFF-NCEP / HIRESAFF-RCAO/ERA40 / RCAO/ERA40-NCEP
cor / bias / / REu / cor / bias / / REu / cor / bias / / REu
DJF / 0.95 / 1.06 / 0.90 / 0.68 / 0.93 / 0.15 / 0.88 / 0.64 / 0.97 / 0.91 / 1.02 / 0.78
MAM / 0.68 / 0.09 / 0.47 / 0.29 / 0.73 / -0.07 / 0.56 / 0.32 / 0.91 / 0.17 / 0.84 / 0.58
JJA / 0.78 / -0.90 / 0.56 / 0.38 / 0.83 / -0.05 / 0.80 / 0.41 / 0.90 / -0.85 / 0.70 / 0.57
SON / 0.93 / 0.34 / 0.73 / 0.60 / 0.89 / -0.09 / 0.91 / 0.54 / 0.93 / 0.43 / 0.81 / 0.59
PREC
[mm] / HIRESAFF-NCEP / HIRESAFF-RCAO/ERA40 / RCAO/ERA40-NCEP
cor / bias / / REu / cor / bias / / REu / cor / bias / / REu
DJF / 0.72 / 21.15 / 1.12 / 0.23 / 0.79 / 8.11 / 0.72 / 0.39 / 0.81 / 13.04 / 1.55 / 0.26
MAM / 0.41 / 2.54 / 0.67 / 0.00 / 0.51 / 1.95 / 0.44 / 0.12 / 0.42 / 0.59 / 1.51 / -0.22
JJA / 0.57 / -18.63 / 0.30 / 0.18 / 0.47 / -13.80 / 0.74 / 0.03 / 0.44 / -4.83 / 0.41 / 0.08
SON / 0.76 / 29.80 / 0.44 / 0.34 / 0.62 / -21.12 / 0.55 / 0.20 / 0.64 / 50.92 / 0.80 / 0.19
TCC
[%] / HIRESAFF-NCEP / HIRESAFF-RCAO/ERA40 / RCAO/ERA40-NCEP
cor / bias / / REu / cor / bias / / REu / cor / bias / / REu
DJF / 0.53 / 21.60 / 0.76 / 0.09 / 0.79 / -0.89 / 0.65 / 0.38 / 0.62 / 22.49 / 1.17 / 0.08
MAM / 0.33 / 11.71 / 0.63 / -0.05 / 0.37 / -1.13 / 0.50 / 0.02 / 0.51 / 12.84 / 1.26 / -0.06
JJA / 0.48 / 10.45 / 0.68 / 0.06 / 0.49 / -0.26 / 0.44 / 0.11 / 0.41 / 10.71 / 1.54 / -0.23
SON / 0.33 / 16.79 / 0.57 / -0.03 / 0.55 / -1.18 / 0.47 / 0.15 / 0.42 / 17.97 / 1.20 / -0.13
RH
[%] / HIRESAFF-NCEP / HIRESAFF-RCAO/ERA40 / RCAO/ERA40-NCEP
cor / bias / / REu / cor / bias / / REu / cor / bias / / REu
DJF / 0.05 / -8.81 / 0.70 / -0.27 / 0.33 / 0.49 / 0.70 / -0.07 / 0.40 / -9.30 / 1.00 / -0.09
MAM / 0.10 / -0.56 / 0.13 / -0.03 / 0.24 / 0.53 / 0.28 / -0.01 / 0.45 / -1.10 / 0.45 / 0.08
JJA / 0.27 / 3.49 / 0.04 / 0.04 / 0.11 / 0.15 / 0.23 / -0.06 / 0.47 / 3.34 / 0.18 / 0.11
SON / -0.06 / -7.00 / 0.25 / -0.15 / 0.41 / 0.30 / 0.51 / 0.04 / 0.35 / -7.30 / 0.50 / 0.00

Table S3.1 Comparison between modeled and observed annual average surface salinity. The table contains mean, standard deviation (SD), bias, root-mean-square error (RMSE), correlation coefficient (r), number of years (nyears) and total number of observations used (nobs). A map with the basin numbers is provided in Figure 1 Electronic Supplementary Material.

Model / Observations
Basin / Mean / SD / Mean / SD / bias / RMSE / r / nyears / nobs
3 / 20.31 / 0.59 / 19.97 / 1.75 / 0.34 / 1.73 / 0.19 / 56 / 733
5 / 12.96 / 0.47 / 12.66 / 1.64 / 0.29 / 1.61 / 0.20 / 50 / 546
6 / 11.51 / 0.42 / 12.54 / 2.83 / -1.03 / 2.87 / -0.01 / 67 / 989
7 / 8.09 / 0.19 / 7.87 / 0.34 / 0.22 / 0.23 / 0.77 / 66 / 1278
8 / 7.52 / 0.19 / 7.50 / 0.27 / 0.01 / 0.16 / 0.83 / 78 / 1986
9 / 7.15 / 0.18 / 7.19 / 0.28 / -0.04 / 0.17 / 0.84 / 83 / 1228
10 / 5.04 / 0.16 / 5.13 / 0.23 / -0.09 / 0.18 / 0.62 / 91 / 476
11 / 3.02 / 0.13 / 3.29 / 0.19 / -0.27 / 0.16 / 0.56 / 77 / 456
12 / 5.45 / 0.23 / 5.51 / 0.28 / -0.06 / 0.15 / 0.85 / 42 / 356
13 / 5.49 / 0.23 / 5.46 / 0.42 / 0.03 / 0.35 / 0.54 / 92 / 982

Table S3.2 Comparison between modeled and observed winter average surface nitrate concentrations. The table contains mean, standard deviation (SD), bias, root-mean-square error (RMSE), correlation coefficient (r), number of years (nyears) and total number of observations used (nobs). A map with the basin numbers is provided in Figure 1 Electronic Supplementary Material.

Model / Observations
Basin / Mean / SD / Mean / SD / bias / RMSE / r / nyears / nobs
3 / 6.28 / 0.74 / 6.36 / 2.21 / -0.08 / 1.87 / 0.59 / 28 / 103
5 / 5.16 / 0.60 / 6.86 / 1.59 / -1.70 / 1.31 / 0.62 / 32 / 78
6 / 5.29 / 0.59 / 6.64 / 1.58 / -1.35 / 1.27 / 0.65 / 32 / 146
7 / 3.68 / 0.41 / 4.07 / 0.87 / -0.40 / 0.85 / 0.28 / 32 / 101
8 / 4.32 / 0.44 / 3.53 / 0.83 / 0.80 / 0.84 / 0.25 / 33 / 299
9 / 4.24 / 0.39 / 3.93 / 0.73 / 0.31 / 0.69 / 0.36 / 33 / 124
10 / 3.82 / 0.31 / 4.37 / 0.70 / -0.55 / 0.58 / 0.58 / 17 / 33
11 / 6.80 / 0.37 / 7.01 / 1.07 / -0.21 / 0.99 / 0.37 / 24 / 77
12 / 9.59 / 3.01 / 11.51 / 3.88 / -1.92 / 3.91 / 0.38 / 20 / 27
13 / 7.42 / 1.14 / 7.17 / 1.98 / 0.25 / 1.92 / 0.34 / 32 / 51

Table S3.3 Comparison between modeled and observed winter average surface phosphate concentrations. The table contains mean, standard deviation (SD), bias, root-mean-square error (RMSE), correlation coefficient (r), number of years (nyears) and total number of observations used (nobs). A map with the basin numbers is provided in Figure 1 Electronic Supplementary Material.

Model / Observations
Basin / Mean / SD / Mean / SD / bias / RMSE / r / nyears / nobs
3 / 0.65 / 0.05 / 0.59 / 0.16 / 0.06 / 0.16 / 0.09 / 28 / 108
5 / 0.55 / 0.04 / 0.72 / 0.19 / -0.18 / 0.19 / -0.02 / 32 / 80
6 / 0.54 / 0.05 / 0.66 / 0.13 / -0.11 / 0.12 / 0.47 / 33 / 145
7 / 0.43 / 0.04 / 0.59 / 0.13 / -0.16 / 0.12 / 0.43 / 32 / 136
8 / 0.48 / 0.06 / 0.61 / 0.13 / -0.14 / 0.13 / 0.28 / 33 / 321
9 / 0.61 / 0.11 / 0.56 / 0.11 / 0.04 / 0.12 / 0.38 / 33 / 152
10 / 0.38 / 0.04 / 0.23 / 0.06 / 0.15 / 0.06 / 0.30 / 18 / 41
11 / 0.12 / 0.02 / 0.05 / 0.04 / 0.07 / 0.04 / 0.05 / 26 / 83
12 / 0.73 / 0.16 / 0.77 / 0.19 / -0.04 / 0.17 / 0.54 / 22 / 31
13 / 0.91 / 0.15 / 0.78 / 0.15 / 0.13 / 0.15 / 0.52 / 32 / 64

Electronic Supplementary Material S4

Comparison between modeled and observed temperatures

A statistical comparison has been made between surface water temperatures observed from Swedish light vessels in the period 1860-1970. The positions of the light vessels are indicated in the map in Figure 1 Electronic Supplementary Material.

The seasonal means from observations are calculated by first computing monthly means for months with at least 15 observations. Then a seasonal mean is computed for years with a monthly mean available for all three months. The overall seasonal mean is simply the arithmetic mean of all years with data. In the tables, standard deviation (STD), bias, correlation (r), unbiased root-mean-square-error (RMSEu) and unbiased residual error (REu) are given, the two latter quantities defined in Electronic Supplementary Material 2.

Table S4.1 Statistical comparison between inter-annual variations of seasonal average surface water temperatures.

DJF / Model / Observations
Mean / SD / Mean / SD / bias / r / RMSEu / REu / noyears / noobs
Falsterborev / 2.05 / 0.66 / 3.21 / 0.62 / -1.16 / 0.69 / 0.51 / 0.18 / 62 / 7833
Finngrundet / 1.73 / 0.50 / 1.90 / 0.39 / -0.17 / 0.70 / 0.36 / 0.07 / 23 / 2346
Fladen / 1.02 / 0.60 / 2.73 / 0.63 / -1.71 / 0.65 / 0.51 / 0.18 / 35 / 5141
Kopparstenarna / - / - / - / - / - / - / - / - / - / -
Landsort / 2.64 / 0.63 / 1.20 / 0.64 / 1.44 / 0.83 / 0.37 / 0.41 / 8 / 664
Oskarsgrundet / 1.31 / 0.67 / 3.06 / 0.63 / -1.75 / 0.77 / 0.44 / 0.30 / 52 / 6798
SvenskaBjörn / 3.35 / 0.61 / 2.69 / 0.57 / 0.66 / 0.85 / 0.33 / 0.43 / 27 / 2793
Svinbådan / 1.15 / 0.69 / 2.62 / 0.68 / -1.47 / 0.79 / 0.44 / 0.34 / 53 / 7263
Sydostbrotten / - / - / - / - / - / - / - / - / - / -
Utklippan / 2.45 / 0.58 / 2.54 / 0.81 / -0.09 / 0.73 / 0.55 / 0.32 / 41 / 3698
MAM / Model / Observations
Mean / SD / Mean / SD / bias / r / RMSEu / REu / noyears / noobs
Falsterborev / 3.80 / 0.74 / 4.52 / 0.89 / -0.72 / 0.78 / 0.56 / 0.37 / 66 / 8809
Finngrundet / 1.54 / 0.42 / 1.92 / 0.38 / -0.38 / 0.32 / 0.47 / -0.22 / 9 / 887
Fladen / 4.67 / 0.73 / 5.73 / 0.85 / -1.06 / 0.84 / 0.46 / 0.46 / 41 / 6213
Kopparstenarna / 3.23 / 0.20 / 3.10 / 0.24 / 0.13 / -0.80 / 0.42 / -0.73 / 3 / 442
Landsort / 3.17 / 0.75 / 2.82 / 0.87 / 0.35 / 0.79 / 0.53 / 0.39 / 18 / 1431
Oskarsgrundet / 4.26 / 0.75 / 5.09 / 0.76 / -0.83 / 0.76 / 0.52 / 0.31 / 55 / 7667
SvenskaBjörn / 3.70 / 0.51 / 2.56 / 0.56 / 1.13 / 0.71 / 0.41 / 0.26 / 17 / 1834
Svinbådan / 4.55 / 0.70 / 5.54 / 0.71 / -0.99 / 0.70 / 0.55 / 0.23 / 58 / 8221
Sydostbrotten / - / - / - / - / - / - / - / - / - / -
Utklippan / 3.59 / 0.87 / 4.45 / 1.08 / -0.85 / 0.74 / 0.73 / 0.33 / 42 / 3862

Table S4.1 cont.