Evaluation of Atmospheric Downward Longwave Radiation in the Brazilian Pampa Region
Abstract
:1. Introduction
2. Materials and Methods
2.1. Site and Instrumentation
2.2. Clearness Index
2.3. Evaluated Parameterizations
2.4. Proposed Model
2.5. Statistical Indexes and Analysis
3. Results and Discussion
3.1. Evaluation of L↓ Models for SMA Site for 2014
3.1.1. Using Original Coefficients—Step 1
3.1.2. Calibrating the Coefficients—Step 2
3.1.3. Calibrating the Coefficients—Step 3
3.1.4. Validation of a New Proposed Downward Longwave Radiation—Step 4
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Original Coefficients | |||||
---|---|---|---|---|---|
Reference | Code | a1 | a2 | a3 | |
Ångströn (1915) [58] | EAN | 0.83 | 0.18 | 0.067 [hPa−1] | |
Brunt (1932) [59] | EBR | 0.52 | 0.065 [hPa−1/2] | - | |
Swinbank (1963) [60] | ESW | 9.36 × 10−6 [K−2] | - | - | |
Idso and Jackson (1969) [13] | EIJ | 0.261 | 0.00077 [K−2] | - | |
Brutsaert (1975) [14] | EBT | 1.24[1/7] | - | - | |
Satterlund (1979) [15] | EST | 1.08 | 1.0 [hPa−1] | - | |
Idso (1981) [16] | EID | 0.7 | 5.95 × 10−5 [hPa−1] | - | |
Garrat (1992) [17] | EGR | 0.79 | 0.17 | 0.96 [hPa−1] | |
Konzelmann (1994) [48] | EKZ | 0.23 | 0.484 [K hPa−1] | 8.00 | |
Prata (1996) [61] | EPR | ; | 1.2 | 3.0 [g−1cm2] | - |
Niemelä (2001) [18] | ENM | 0.72 | 0.009; if 2 −0.076; if 2 [hPa−1] | - |
Reference | Code | C(Kt) |
---|---|---|
Black (1956) [51] | CQB | |
Campbell (1985) [52] | CCB | |
Wheishampel and Urban (1996) [54] | CWU |
Entire Period | CS | CP | CD | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
R2 | RMSE (Wm−2) | PBias (%) | R2 | RMSE (Wm−2) | PBias (%) | R2 | RMSE (Wm−2) | PBias (%) | R2 | RMSE (Wm−2) | PBias (%) | |
EAN | 0.59 | 44.79 | −9.71 | 0.73 | 29.54 | −5.23 | 0.62 | 45.26 | −10.21 | 0.59 | 59.78 | −14.50 |
EBR | 0.67 | 50.42 | −11.49 | 0.78 | 38.590 | −8.53 | 0.68 | 49.60 | −11.17 | 0.65 | 64.69 | −15.70 |
EGR | 0.54 | 55.10 | −12.67 | 0.69 | 36.54 | −7.77 | 0.59 | 56.64 | −13.43 | 0.54 | 72.03 | −17.61 |
ENM | 0.67 | 30.92 | −3.47 | 0.78 | 26.61 | −0.32 | 0.68 | 30.06 | −3.03 | 0.64 | 37.55 | −8.13 |
ESW | 0.53 | 51.65 | −10.85 | 0.69 | 37.17 | −6.07 | 0.59 | 51.10 | −11.06 | 0.53 | 68.12 | −16.48 |
EIJ | 0.53 | 49.93 | −10.20 | 0.67 | 35.47 | −5.26 | 0.59 | 49.27 | −10.41 | 0.52 | 66.44 | −16.01 |
EBT | 0.66 | 38.57 | −7.75 | 0.77 | 28.24 | −4.36 | 0.67 | 37.72 | −7.65 | 0.65 | 50.98 | −12.16 |
EST | 0.61 | 35.87 | −6.57 | 0.74 | 24.77 | −2.15 | 0.64 | 35.14 | −6.90 | 0.60 | 48.66 | −11.56 |
EID | 0.70 | 25.48 | −2.18 | 0.79 | 22.91 | 0.87 | 0.69 | 24.56 | −1.97 | 0.66 | 30.30 | −6.34 |
EPR | 0.65 | 38.87 | −7.89 | 0.77 | 27.51 | −4.25 | 0.67 | 38.19 | −7.90 | 0.64 | 51.88 | −12.42 |
EKZ | 0.62 | 141.64 | −36.75 | 0.75 | 122.68 | −33.84 | 0.66 | 144.85 | −36.97 | 0.61 | 160.07 | −40.03 |
Entire Period | CS | CP | CD | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
R2 | RMSE | PBias | R2 | RMSE | PBias | R2 | RMSE | PBias | R2 | RMSE | PBias | |||||
EAN | 0.94/0.21/0.04 | 0.61 | 26.03 | 0.15 | 5.34/4.52/2.22 × 10−4 | 0.73 | 23.21 | 0.23 | 0.94/0.06/0.02 | 0.61 | 22.90 | 0.06 | 0.97/1.14/0.13 | 0.61 | 16.05 | 0.03 |
EBR | 0.77/0.03/- | 0.61 | 26.13 | 0.15 | 0.78/0.02/- | 0.73 | 23.26 | 0.21 | 0.87/0.01/- | 0.61 | 22.90 | 0.06 | 0.87/0.02/- | 0.59 | 16.49 | 0.03 |
ESW | 1.05 × 10−5/--/- | 0.53 | 34.25 | 0.13 | 9.99 × 10−6/-/- | 0.69 | 32.69 | 0.31 | 1.05 × 10−5/-/- | 0.59 | 31.34 | 0.08 | 1.12 × 10−5/-/- | 0.53 | 21.18 | 0.03 |
EIJ | 0.08/−3.76 × 10−4/- | 0.54 | 26.81 | −0.07 | 0.14/−1.22 × 10−4/- | 0.68 | 24.05 | 0.02 | 0.07/−5.0 × 10−4/- | 0.59 | 22.37 | −0.07 | 0.02/−1.3 × 10−3/- | 0.55 | 16.40 | −0.03 |
EBT | 1.35/-/- | 0.66 | 26.60 | 0.19 | 1.30/-/- | 0.77 | 24.92 | 0.33 | 1.34/-/- | 0.67 | 25.29 | 0.11 | 1.41/-/- | 0.65 | 17.92 | 0.05 |
EST | 2.94/5.57 × 10−5/- | 0.67 | 23.55 | −0.06 | 2.96/3.75 × 10−5/- | 0.77 | 20.91 | −0.22 | 0.91/1.47 × 107/- | 0.59 | 23.02 | 0.02 | 4.49/2.72 × 10−6/- | 0.66 | 14.72 | −0.05 |
EID | 0.77/4.54 × 10−5/- | 0.67 | 24.24 | 0.16 | 0.76/3.40 × 10−5/- | 0.76 | 21.88 | 0.24 | 0.83/2.46 × 10−5/- | 0.65 | 22.13 | 0.08 | 0.87/2.59 × 10−5/- | 0.62 | 15.96 | 0.04 |
EGR | 0.90/7.43/7.91 | 0.54 | 27.25 | 0.01 | 0.86/−4.91/10.57 | 0.69 | 24.06 | 0.09 | 0.91/8.16/7.06 | 0.59 | 23.02 | 0.02 | 0.96/8.30/6.87 | 0.54 | 16.84 | −0.09 |
EKZ | 0.90/−5.15/0.12 | 0.54 | 27.25 | 0.01 | 0.86/−5.76/0.07 | 0.69 | 24.06 | 0.09 | 0.86/0.24/1.82 | 0.62 | 22.83 | 0.06 | 0.96/−4.86/0.06 | 0.54 | 16.84 | −0.01 |
EPR | 2.07/4.08/- | 0.63 | 25.82 | 0.18 | 3.65/2.59/- | 0.73 | 23.02 | 0.20 | 5.97/2.83/- | 0.62 | 22.83 | 0.07 | −0.58/7.23/- | 0.62 | 16.24 | 0.13 |
ENM | 0.84/3.60 × 10−3/- | 0.61 | 26.20 | 0.14 | 0.82/2.5 × 10−3/- | 0.73 | 23.18 | 0.22 | 0.89/1.2 x10−3/- | 0.61 | 22.90 | 0.06 | 0.92/2.1 × 10−3/- | 0.58 | 16.55 | 0.02 |
EAI | −0.20/−0.07/1.05 | 0.72 | 21.16 | −0.03 | −0.15/−0.07/0.98 | 0.82 | 18.18 | −0.02 | −0.22/−0.29/1.12 | 0.71 | 18.72 | −0.05 | −0.22/−0.40/1.18 | 0.67 | 14.06 | −0.02 |
a1 | a2 | a3 | μ | λ | R2 | RMSE (Wm−2) | Pbias (%) | |
---|---|---|---|---|---|---|---|---|
Entire Period | ||||||||
EST_CQB | 5.45 | 2.76 × 10−7 | - | 0.13 | 0.95 | 0.78 | 17.82 | −0.06 |
EBT_CQB | 1.27 | - | - | 0.14 | 1.44 | 0.76 | 22.40 | −0.39 |
EID_CQB | 0.76 | 2.71 × 10−5 | - | 0.15 | 1.10 | 0.75 | 19.73 | −0.16 |
EST_CCB | 4.96 | 2.29 × 10−7 | - | 0.07 | 0.56 | 0.73 | 17.52 | −0.14 |
EKZ_CQB | 0.68 | 0.32 | 3.85 | 0.17 | 1.01 | 0.73 | 20.48 | −0.17 |
CS | ||||||||
EST_CCB | 4.81 | 8.46 × 10−7 | - | 0.27 | 1.19 | 0.80 | 18.06 | −0.07 |
EST_CQB | 3.80 | 4.44 × 10−6 | - | 0.14 | 1.12 | 0.79 | 19.28 | −0.09 |
EBT_CCB | 1.29 | - | - | 443.41 | 84.01 | 0.79 | 23.42 | −0.52 |
EID_CCB | 0.76 | 3.42 × 10−5 | - | 28.53 | 3.51 | 0.79 | 19.46 | −0.20 |
EBT_CQB | 1.18 | - | - | 0.11 | 0.09 | 0.79 | 23.20 | −0.47 |
CP | ||||||||
EST_CQB | 3.19 | 1.42 × 10−7 | - | 1.10 | 0.13 | 0.72 | 18.52 | −0.07 |
EST_CCB | 3.55 | 8.23 × 10−6 | - | 0.08 | 0.72 | 0.71 | 19.49 | −0.17 |
EBT_CQB | 1.29 | - | - | 0.21 | 2.49 | 0.71 | 23.76 | −0.42 |
EBT_CCB | 1.30 | - | - | 0.06 | 1.42 | 0.71 | 23.76 | −0.42 |
EID_CCB | 0.80 | 2.36 × 10−5 | - | 0.06 | 1.15 | 0.69 | 20.71 | −0.17 |
CD | ||||||||
EST_CWU | 0.94 | 8.18 × 10−8 | - | 0.52 | 0.49 | 0.68 | 14.00 | −0.17 |
EST_CQB | 1.92 | 8.71 × 10−6 | - | 1.06 | 0.20 | 0.68 | 14.58 | −0.08 |
EBT_CQB | 2.58 | - | - | −0.44 | −0.15 | 0.67 | 17.31 | −0.19 |
EBT_CCB | 1.39 | - | - | 0.00 | 4.36 | 0.67 | 17.27 | −0.18 |
EST_CCB | 1.97 | 1.69 × 10−4 | - | 0.32 | 0.28 | 0.67 | 15.25 | −0.12 |
a1 | a2 | a3 | μ | λ | R2 | RMSE (Wm−2) | PBias (%) | |
---|---|---|---|---|---|---|---|---|
Entire Period | ||||||||
EAI_CQB | −0.17 | −0.25 | 1.01 | 0.13 | 1.12 | 0.79 | 17.23 | −0.01 |
EAI_CCB | −0.19 | −0.31 | 1.06 | 0.06 | 0.71 | 0.75 | 16.63 | 0.00 |
EAI_CWU | −0.02 | −0.01 | 0.09 | 0.04 | 1.01 | 0.72 | 20.80 | −0.02 |
CS | ||||||||
EAI_CCB | −0.16 | −0.22 | 1.02 | 1.75 | 2.35 | 0.83 | 16.46 | 0.00 |
EAI_CWU | −0.01 | −0.01 | 0.07 | 0.09 | 0.90 | 0.82 | 18.01 | −0.01 |
EAI_CQB | −0.14 | −0.12 | 0.97 | 1.47 | 3.39 | 0.82 | 17.89 | −0.04 |
CP | ||||||||
EAI_CCB | −0.20 | −0.30 | 1.04 | 0.09 | 0.47 | 0.74 | 17.68 | 0.00 |
EAI_CQB | −0.19 | −0.28 | 0.97 | 0.21 | 0.55 | 0.74 | 17.69 | 0.00 |
EAI_CWU | −0.02 | −0.03 | 0.10 | 0.03 | 1.05 | 0.71 | 18.57 | −0.01 |
CD | ||||||||
EAI_CCB | −0.21 | −0.38 | 1.14 | 0.01 | 2.44 | 0.69 | 13.82 | 0.00 |
EAI_CQB | −0.21 | −0.38 | 1.14 | 0.04 | 4.54 | 0.69 | 13.82 | 0.00 |
EAI_CWU | −0.19 | −0.36 | 1.02 | 0.27 | −0.11 | 0.68 | 14.10 | 0.00 |
L↓ (Wm−2) | RMSE (Wm−2) | R2 | PBias (%) | |
---|---|---|---|---|
SMA (1 January 2015 to 31 December 2019) | ||||
EAI | 381.49 | 22.84 | 0.69 | 1.54 |
EAI_CQB | 383.45 | 18.59 | 0.79 | 1.44 |
EAI_CCB | 389.96 | 18.37 | 0.76 | 1.46 |
EAI_CWU | 381.34 | 22.75 | 0.70 | 1.50 |
ESTorig | 354.55 | 33.71 | 0.60 | −5.62 |
ESTcal | 407.53 | 40.65 | 0.66 | 8.47 |
EST_CQB | 383.11 | 18.52 | 0.78 | 1.35 |
EST_CCB | 340.09 | 47.58 | 0.75 | −11.51 |
EST_CWU | 381.53 | 22.57 | 0.70 | 1.55 |
CAS (20 February 2013 to 16 April 2016) | ||||
EAI | 379.88 | 25.33 | 0.67 | 1.33 |
EAI_CQB | 388.00 | 20.47 | 0.76 | 1.07 |
EAI_CCB | 392.65 | 20.75 | 0.72 | 1.01 |
EAI_CWU | 388.06 | 25.04 | 0.70 | 1.91 |
ESTorig | 361.33 | 32.60 | 0.61 | −5.10 |
ESTcal | 415.34 | 42.50 | 0.66 | 9.08 |
EST_CQB | 387.80 | 20.19 | 0.76 | 1.02 |
EST_CCB | 342.82 | 50.44 | 0.71 | −11.80 |
EST_CWU | 387.60 | 25.03 | 0.69 | 1.79 |
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Aimi, D.; Zimmer, T.; Buligon, L.; de Arruda Souza, V.; Hernandez, R.; Romio, L.; Rubert, G.C.; Diaz, M.B.; Maldaner, S.; Veeck, G.P.; et al. Evaluation of Atmospheric Downward Longwave Radiation in the Brazilian Pampa Region. Atmosphere 2021, 12, 28. https://doi.org/10.3390/atmos12010028
Aimi D, Zimmer T, Buligon L, de Arruda Souza V, Hernandez R, Romio L, Rubert GC, Diaz MB, Maldaner S, Veeck GP, et al. Evaluation of Atmospheric Downward Longwave Radiation in the Brazilian Pampa Region. Atmosphere. 2021; 12(1):28. https://doi.org/10.3390/atmos12010028
Chicago/Turabian StyleAimi, Daniele, Tamires Zimmer, Lidiane Buligon, Vanessa de Arruda Souza, Roilan Hernandez, Leugim Romio, Gisele Cristina Rubert, Marcelo Bortoluzzi Diaz, Silvana Maldaner, Gustavo Pujol Veeck, and et al. 2021. "Evaluation of Atmospheric Downward Longwave Radiation in the Brazilian Pampa Region" Atmosphere 12, no. 1: 28. https://doi.org/10.3390/atmos12010028