Introduction
Model | MBE (%) | Main inputs | Testing locations |
---|---|---|---|
8.0 | Air mass, surface albedo, surface air pressure, precipitable water vapor, ozone | Sun-photometric sites | |
5.0 | Surface albedo, surface air pressure, precipitable water vapor, cloud observations | US | |
5.0 | Surface air pressure, Linke index | Europe | |
2.0 | Atmospheric aerosol optical depth, precipitable water vapor | Europe | |
5.0 | Cloud observations, aerosol optical depth, precipitable water vapor, ozone, surface albedo, snow depth, days-since-last snowfall, atmospheric pressure | US | |
5.0 | Sunshine fraction, dry- and wet-bulb temperature | UK, Japan, Europe | |
NSRDB—SUNY [13] | 5.0 | Meteorological satellite images | US |
− 5.0 | Surface air pressure, precipitable water vapor, ozone | Sun-photometric sites | |
5.0 | Precipitable water vapor, ozone, surface albedo, aerosol albedo, atmospheric pressure | Sun-photometric sites | |
− 4.5 | Linke index | Spain | |
− 4.5 | Linke index | Spain | |
− 25.0 | Direct atmospheric transmissivity, diffuse fraction (default values) | Spain | |
10.0 | Monthly average sunshine fraction and cloudiness data | Spain | |
Zelenka [22] | 10.0 | Meteorological satellite images | Switzerland, US |
Methods
TRAD (temperature-estimation of radiation) daily model
Daily atmospheric transmissivity and diffuse fraction models
Daily atmospheric transmissivity | Day classification |
---|---|
Daily atmospheric transmissivity \(\le\) 0.30 | cloudy |
0.30 \(<\) daily atmospheric transmissivity \(<\) 0.50 | partly cloudy |
Daily atmospheric transmissivity \(\ge\) 0.50 | sunny and clear |
Application of solar analyst
Observed daily atmospheric transmissivity
Hourly solar radiation model
Data availability for verification
Site Name | Latitude | Longitude | Elevation (m) | Time Zone | Installed |
---|---|---|---|---|---|
Bondville, IL | 40.0519°N | 88.3731°W | 230 | UTC-6 | April 1994 |
Boulder, CO | 40.1249°N | 105.2368°W | 1689 | UTC-7 | July 1995 |
Desert Rock, NV | 36.6237°N | 116.0195°W | 1007 | UTC-8 | March 1998 |
Fort Peck, MT | 48.3078°N | 105.1017°W | 634 | UTC-7 | November 1994 |
Goodwin Creek, MS | 34.2547°N | 89.8729°W | 98 | UTC-6 | December 1994 |
Penn State, PA | 40.7201°N | 77.9309°W | 376 | UTC-5 | June 1998 |
Sioux Falls, SD | 43.7340°N | 96.6233°W | 473 | UTC-6 | June 2003 |
Site Name | Time period | Total years | Missing data (%) |
---|---|---|---|
Bondville, IL | Jan 1996 to Dec 1998 and Jan 2000 to Dec 2015 | 19 | 0.32 |
Boulder, CO | Jan 1996 to Dec 2015 | 20 | 0.05 |
Desert Rock, NV | Jan 1999 to Dec 2011 and Jan 2013 to Dec 2015 | 16 | 0.82 |
Fort Peck, MT | Jan 1997 to Dec 2015 | 19 | 0.61 |
Goodwin Creek, MS | Jan 1996 to Dec 2002 and Jan 2005 to Dec 2015 | 18 | 0.71 |
Penn State, PA | Jan 1999 to Dec 2015 | 17 | 1.50 |
Sioux Falls, SD | Jan 2004 to Dec 2006 and Jan 2008 to Dec 2015 | 11 | 0.10 |
Statistical validation methods
Results and discussion
All years
Daily radiation verification
Station Name | Daily atmospheric transmissivity | Daily irradiance |
n
| ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
MBE | MABE |
r
| MBE | MABE |
r
| ||||||
(%) | (%) | (%) | (W m−2) | (%) | (W m−2) | ||||||
All sky conditions | |||||||||||
Bondville, IL | 6.10 | 0.03 | 26.80 | 0.13 | 0.57** | 0.40 | 0.74 | 27.50 | 45.96 | 0.82** | 6918 |
Boulder, CO | − 3.20 | − 0.02 | 23.00 | 0.13 | 0.35** | 3.30 | 6.35 | 27.70 | 52.63 | 0.78** | 7301 |
Desert Rock, NV | − 12.50 | − 0.08 | 19.00 | 0.13 | 0.45** | − 10.30 | − 24.25 | 17.30 | 40.65 | 0.88** | 5796 |
Fort Peck, MT | 20.0 | 0.09 | 33.00 | 0.15 | 0.46** | -2.50 | -3.90 | 24.80 | 39.87 | 0.88** | 6897 |
Goodwin Creek, MS | 5.80 | 0.03 | 23.00 | 0.11 | 0.62** | 3.10 | 5.60 | 24.40 | 44.59 | 0.80** | 6528 |
Penn State, PA | 10.10 | 0.05 | 29.70 | 0.14 | 0.61** | 9.60 | 14.86 | 30.30 | 47.02 | 0.84** | 6116 |
Sioux Falls, SD | 8.60 | 0.04 | 32.20 | 0.16 | 0.13** | 1.50 | 2.50 | 27.00 | 44.87 | 0.83** | 4013 |
Combined data from all stations | 3.77 | 0.02 | 25.10 | 0.13 | 0.50** | 0.28 | 0.49 | 25.27 | 45.26 | 0.83** | 43569 |
Daily atmospheric transmissivity ≤ 0.30 (Cloudy sky) | |||||||||||
Bondville, IL | 108.0 | 0.19 | 130.2 | 0.23 | 0.12** | 89.1 | 44.73 | 111.10 | 55.77 | 0.62** | 1503 |
Boulder, CO | 135.05 | 0.26 | 148.73 | 0.28 | NSS | 145.77 | 89.29 | 157.89 | 96.70 | 0.45** | 599 |
Desert Rock, NV | 127.05 | 0.23 | 138.81 | 0.26 | NSS | 143.53 | 74.73 | 155.15 | 80.78 | 0.41** | 209 |
Fort Peck, MT | 108.11 | 0.22 | 124.99 | 0.25 | 0.22** | 41.75 | 21.74 | 77.98 | 40.61 | 0.67** | 1335 |
Goodwin Creek, MS | 119.97 | 0.19 | 136.73 | 0.22 | 0.06* | 106.02 | 52.04 | 124.72 | 61.22 | 0.36** | 1309 |
Penn State, PA | 90.24 | 0.16 | 115.44 | 0.20 | 0.14** | 76.50 | 38.88 | 102.46 | 52.07 | 0.55** | 1589 |
Sioux Falls, SD | 198.17 | 0.36 | 201.09 | 0.37 | 0.10** | 90.78 | 51.20 | 115.01 | 64.87 | 0.63** | 665 |
Combined data from all stations | 117.65 | 0.21 | 135.58 | 0.24 | 0.15** | 87.79 | 45.68 | 111.65 | 58.09 | 0.55** | 7209 |
0.30 \({ < }\;{\text{daily atmospheric transmissivity}}\;{ < }\) 0.50 (Partly cloudy sky) | |||||||||||
Bondville, IL | 22.16 | 0.08 | 38.44 | 0.15 | 0.18** | 18.33 | 24.40 | 36.51 | 48.62 | 0.84** | 1409 |
Boulder, CO | 24.1 | 0.10 | 36.47 | 0.15 | 0.12** | 33.76 | 46.98 | 44.79 | 62.34 | 0.85** | 1363 |
Desert Rock, NV | 20.88 | 0.08 | 35.18 | 0.15 | 0.15** | 23.30 | 29.86 | 36.82 | 47.18 | 0.83** | 429 |
Fort Peck, MT | 34.50 | 0.14 | 48.49 | 0.19 | 0.17** | − 5.76 | − 6.32 | 38.78 | 42.55 | 0.87** | 2313 |
Goodwin Creek, MS | 20.68 | 0.08 | 33.51 | 0.14 | 0.20** | 19.84 | 29.41 | 33.40 | 49.51 | 0.78** | 1180 |
Penn State, PA | 17.04 | 0.06 | 38.26 | 0.15 | 0.22** | 17.84 | 22.92 | 38.48 | 49.45 | 0.82** | 1598 |
Sioux Falls, SD | 33.98 | 0.13 | 45.93 | 0.18 | NSS | 18.20 | 22.36 | 40.60 | 49.90 | 0.85** | 805 |
Combined data from all stations | 25.48 | 0.10 | 40.49 | 0.16 | 0.16** | 15.96 | 20.43 | 38.60 | 49.44 | 0.85** | 9097 |
Daily atmospheric transmissivity ≥ 0.50 (Sunny and clear sky) | |||||||||||
Bondville, IL | − 7.49 | − 0.04 | 13.90 | 0.09 | 0.22** | − 10.86 | − 24.25 | 18.57 | 41.47 | 0.90** | 4006 |
Boulder, CO | − 12.05 | − 0.08 | 16.92 | 0.11 | 0.15** | − 6.15 | − 13.35 | 20.84 | 45.24 | 0.90** | 5339 |
Desert Rock, NV | − 15.53 | − 0.11 | 16.99 | 0.12 | 0.27** | − 12.81 | − 32.22 | 15.40 | 38.72 | 0.92** | 5158 |
Fort Peck, MT | 1.16 | 0.01 | 13.28 | 0.08 | 0.23** | − 5.34 | − 12.91 | 15.60 | 37.72 | 0.87** | 3249 |
Goodwin Creek, MS | − 6.16 | − 0.04 | 11.82 | 0.08 | 0.30** | − 6.84 | − 16.12 | 16.05 | 37.81 | 0.88** | 4039 |
Penn State, PA | − 4.31 | − 0.03 | 13.90 | 0.09 | 0.28** | − 1.16 | − 2.61 | 19.03 | 42.78 | 0.89** | 2929 |
Sioux Falls, SD | − 10.64 | − 0.06 | 16.70 | 0.10 | 0.10** | − 7.90 | − 16.50 | 18.11 | 37.83 | 0.92** | 2543 |
Combined data from all stations | − 8.86 | − 0.05 | 15.02 | 0.10 | 0.19** | − 7.87 | − 18.13 | 17.63 | 40.61 | 0.89** | 27263 |
Daily atmospheric transmissivity verification
Year 2015
Daily radiation verification
Station name | Daily atmospheric transmissivity | Daily irradiance |
n
| ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
MBE | MABE |
r
| MBE | MABE |
r
| ||||||
(%) | (%) | (%) | (W m−2) | (%) | (W m−2) | ||||||
All sky conditions | |||||||||||
Bondville, IL | 5.49 | 0.03 | 39.75 | 0.20 | NSS | − 0.58 | − 0.97 | 27.49 | 46.50 | 0.81** | 365 |
Boulder, CO | − 1.93 | − 0.01 | 22.05 | 0.12 | 0.50** | 5.42 | 10.02 | 28.14 | 52.07 | 0.80** | 365 |
Desert Rock, NV | − 10.07 | − 0.06 | 17.85 | 0.11 | 0.42** | − 5.99 | − 13.75 | 16.10 | 36.96 | 0.87** | 363 |
Fort Peck, MT | 22.25 | 0.11 | 33.66 | 0.15 | 0.50** | 0.31 | 0.49 | 22.64 | 36.03 | 0.88** | 362 |
Goodwin Creek, MS | 8.36 | 0.04 | 22.07 | 0.10 | 0.72** | 7.25 | 12.80 | 23.93 | 42.28 | 0.83** | 364 |
Penn State, PA | 10.84 | 0.05 | 29.86 | 0.14 | 0.57** | 9.61 | 15.15 | 31.00 | 48.84 | 0.82** | 365 |
Sioux Falls, SD | 7.03 | 0.04 | 31.55 | 0.16 | 0.18** | 2.05 | 3.39 | 28.07 | 46.54 | 0.81** | 365 |
Combined data from all stations | 5.23 | 0.03 | 27.51 | 0.14 | 0.44** | 2.19 | 3.89 | 24.89 | 44.15 | 0.83** | 2549 |
Daily atmospheric transmissivity ≤ 0.30 (Cloudy sky) | |||||||||||
Bondville, IL | 181.88 | 0.31 | 197.90 | 0.34 | NSS | 79.23 | 37.31 | 105.08 | 49.48 | 0.70** | 72 |
Boulder, CO | 80.19 | 0.16 | 93.65 | 0.18 | NSS | 87.81 | 58.79 | 100.27 | 67.13 | 0.42** | 39 |
Desert Rock, NV | 120.71 | 0.26 | 124.55 | 0.27 | NSS | 114.58 | 69.23 | 117.61 | 71.05 | 0.80** | 13 |
Fort Peck, MT | 121.85 | 0.23 | 141.60 | 0.27 | 0.34** | 54.45 | 25.46 | 94.30 | 44.09 | 0.72** | 73 |
Goodwin Creek, MS | 90.68 | 0.15 | 108.50 | 0.18 | NSS | 82.64 | 46.45 | 100.43 | 56.45 | 0.55** | 85 |
Penn State, PA | 105.79 | 0.19 | 121.69 | 0.22 | 0.25* | 77.68 | 40.07 | 98.18 | 50.65 | 0.66** | 93 |
Sioux Falls, SD | 228.56 | 0.38 | 228.56 | 0.38 | NSS | 119.93 | 57.59 | 141.50 | 67.95 | 0.64** | 54 |
Combined data from all stations | 130.29 | 0.24 | 144.72 | 0.26 | 0.14** | 82.78 | 43.16 | 105.03 | 54.76 | 0.63** | 431 |
0.30 \({ < }\quad {\text{daily atmospheric transmissivity}}\;{ < }\) 0.50 (Partly cloudy sky) | |||||||||||
Bondville, IL | 33.93 | 0.13 | 51.27 | 0.20 | − 0.24* | 23.74 | 35.40 | 34.09 | 50.83 | 0.84** | 84 |
Boulder, CO | 28.00 | 0.12 | 42.96 | 0.18 | NSS | 39.20 | 50.90 | 54.47 | 70.73 | 0.84** | 71 |
Desert Rock, NV | 20.53 | 0.08 | 32.23 | 0.13 | NSS | 26.76 | 38.13 | 36.88 | 52.54 | 0.83** | 33 |
Fort Peck, MT | 38.08 | 0.15 | 46.14 | 0.18 | NSS | − 4.13 | − 4.75 | 31.57 | 36.33 | 0.90** | 124 |
Goodwin Creek, MS | 25.85 | 0.10 | 36.20 | 0.14 | 0.28* | 27.26 | 38.95 | 38.81 | 55.46 | 0.83** | 69 |
Penn State, PA | 13.11 | 0.05 | 35.72 | 0.14 | 0.24* | 15.39 | 20.47 | 36.50 | 48.55 | 0.84** | 95 |
Sioux Falls, SD | 29.65 | 0.11 | 44.26 | 0.17 | NSS | 19.71 | 25.42 | 37.31 | 48.11 | 0.85** | 81 |
Combined data from all stations | 28.18 | 0.11 | 42.42 | 0.17 | NSS | 18.95 | 25.06 | 37.83 | 50.03 | 0.85** | 555 |
Daily atmospheric transmissivity ≥ 0.50 (Sunny and clear sky) | |||||||||||
Bondville, IL | − 17.23 | − 0.11 | 22.78 | 0.15 | NSS | − 13.13 | − 28.78 | 19.95 | 43.73 | 0.90** | 209 |
Boulder, CO | − 10.75 | − 0.07 | 15.24 | 0.10 | 0.21** | − 4.03 | − 8.81 | 20.40 | 44.57 | 0.91** | 255 |
Desert Rock, NV | − 13.58 | − 0.09 | 15.63 | 0.11 | 0.19** | − 9.19 | − 22.56 | 13.82 | 33.94 | 0.92** | 317 |
Fort Peck, MT | 5.18 | 0.03 | 12.18 | 0.07 | NSS | − 2.73 | − 6.61 | 13.32 | 32.24 | 0.88** | 165 |
Goodwin Creek, MS | − 3.9 | − 0.02 | 10.05 | 0.06 | 0.28** | − 3.98 | − 9.40 | 13.62 | 32.22 | 0.91** | 210 |
Penn State, PA | − 4.36 | − 0.02 | 13.96 | 0.09 | 0.16* | − 0.45 | − 1.02 | 21.12 | 48.02 | 0.83** | 177 |
Sioux Falls, SD | − 11.14 | − 0.07 | 16.96 | 0.11 | 0.19** | − 8.28 | − 17.08 | 19.85 | 40.97 | 0.90** | 230 |
Combined data from all stations | − 9.15 | − 0.06 | 15.46 | 0.10 | 0.11** | − 6.33 | − 14.45 | 17.18 | 39.20 | 0.89** | 1563 |