Table 1.

Statistics to compare estimation methods using hard and soft data versus using hard data only. The analysis uses a constant mean trend, and compares statistics for different cross-validation radii of exclusion points

Stat	rv=10	rv=30	rv=50	rv=100
MEs	−1.1407E-03	−1.0634E-03	−9.1051E-04	−8.9985E-04
MEh	−4.5917E-04	−2.7240E-04	5.0473E-05	1.6704E-04
MSEs	2.5634E-04	2.8936E-04	3.3093E-04	4.1262E-04
MSEh	2.6021E-04	3.1216E-04	3.9202E-04	5.7070E-04
PCMSE	−1.4863	−7.3057	−15.5833	−27.6988
MaxRE	−27.2217	−27.2217	−33.8706	−44.2374
Pval	0.2117	<0.0001	<0.0001	<0.0001
P01	4.6512	13.9535	18.6047	74.4186
P05	13.9535	23.2558	44.1861	90.6977
P1	16.2791	27.9070	53.4884	100.0000

r_v is the cross-validation radius (km) around monitoring stations within which all observation points are excluded in the cross-validation estimation

MEs is the mean error using soft data

MSEs is the mean square error using soft data

MEh is the mean error using hard data only

MSEh is the mean square error using hard data only

PCMSE is the percent change in mean square error = (MSEs-MSEh)/MSEh*100;

MaxRE is the maximum achieved relative reduction error at a station (soft compared to hard)

Pval is the p-value testing the hypothesis that there is no difference between the mean square errors using soft vs. hard data

P01 is the percentage of stations with a significant reduction in error with a p value less or equal to 0.01

P05 is the percentage of stations with a significant reduction in error with a p value less or equal to 0.05

P1 is the percentage of stations with a significant reduction in error with a p value less or equal to 0.1