This deals with the assessment of several parameterizations of longwave radiation. The parametes were calibrated using a calibration tool on Ameriflux data.

1. Introduction
Downwelling (DL) and upwelling (UL) longwave atmospheric radiation are very important components of the global radiation balance. They influence many hydrological processes, such as evapotranspiration,
soil-surface temperature, energy balance, and snowmelt. Since field measurements of DL and UL are extremely rare, many simplified formulations have been proposed in order to model DL and UL by using
easily available meteorological observations such as air temperature, relative humidity, incoming solar radiation and cloud cover. Ten of those formulations were integrated in the GIS based hydrological model
NewAge-Jgrass (Formetta et al., 2014), and tested against field measurement data at hourly timestep.
Components of longwave atmospheric
radiation : NewAge-LWRB
Marialaura Bancheri1, Giuseppe Formetta2, Wuletawu Abera1 & Riccardo Rigon1
1Dept. of Civil, Environmental and Mechanical Engineering, University of Trento, 77 Mesiano St., 38123 Trento, Italy
2Dept. of Civil and Environmental Engineering, University of Calabria,Rende (CS),Italy
PhD Days di Ingegneria delle
Acque
Bologna 30 Giugno-2Luglio 2014
Fig.3: Measurments from 6 Ameriflux stations and from 1 CSU
station were used to test the system.
NewAge-LWRB package: methodology
Simplified formulations for DL and UL are based on the Stefan-Boltzmann equation:
DL = ε all-sky Ÿ σ Ÿ Ta
4 (1) , UL = ε s Ÿ σ Ÿ Ts
4 (2)
where σ [W m-2 K-4] is the Stefan-Boltzmann constant, Ta [K] is the near-surface air temperature, ε all-sky [-] is the atmosphere effective emissivity, ε s [-] is the soil emissivity and Ts [K] is the surface soil
temperature. ε all-sky is formulated according to eq. (3), to take into account the increase of DL in cloud cover conditions :
ε all-sky = [ ε clear- 0.035 Ÿ (z/1000) ] Ÿ (1+aŸcb) (3)
where c [-] is the cloud cover fraction , z is the elevation [m] and a and b are two calibration coefficients, Fig.1.
Being the coefficient X, Y and Z of models in Table (1) strictly related to the location, in order to obtain site-specific values, we optimized them to fit DL measurements data, using LUCA calibration algorithm
(Hay et al., 2006), which is part NewAge-Jgrass,Fig.2. The calibration procedure follows these steps:
-Step 1: Computation of the theoretical solar radiation at the top atmosphere (Itop), using the NewAge-shortwave radiation balance component (Formetta et. al., 2013) ;
-Step 2: Computation of the c, as a ratio between the measured incoming solar radiation (Im) and Itop.
-Step 3: Calibration of the parameters X, Y and Z;
-Step 4: Calibration of the parameters a and b;
Table 1. 10 clear sky emissivity formulations were implemented in the
LWRB-package
Applications and results
The NewAge-LWRB package was tested in different stations in the USA, Fig.3. For each station shortwave, longwave upwelling and downwelling radiation, precipitation, air temperature and relative humidity
measurements were available.
Fig.4 shows the results of the models verification. For 3 of 7 stations the scatter plots of measured and simulated DL are shown and is computed a classical goodness of fit index: Kling-Gupta Efficiency. For
each station and each model, the calibration of the site-specific parameters lead to higher values of the KGE index (KGE opt) then the classic formulation (KGE classic).
Fig 2. NewAge-Jgrass architecture
Fig.4: The scatter plots and the values of the KGE index show that the calibration, especially for some models, allows to obtain more
accurate simulations of DL than the classical formulations.
Conclusions
The NewAge-LWRB package is integrated into the NewAge-JGrass hydrological model as an OMS3 component, allowing the use of all the other OMS3 components: GIS-based visualization, automatic
calibration algorithm and evaluation packages. The results of the application of that package show that site-specific parameters of the simplified formulations allow to obtain values of the simulated longwave
radiation really close to the measured ones, optimizing the efficiency of the formulations, in comparison with their classical forms. The work will continue with the calibration of the parameters for many other
US stations in order to obtain some relationships between the climatic, atmospheric and hydrological conditions of the sites and values of the parameters.
References
Angstrom, A. (1918), A study of the radiation of the atmosphere, Smithson. Misc. Collect., 65, 1 –159.
Brunt, D. (1932), Notes on radiation in the atmosphere, Q. J. R. Meteorol. Soc., 58, 389–420.
Brutsaert, W. (1975), On a derivable formula for long-wave radiation from clear skies, Water Resour. Res., 11, 742– 744.
Dilley, A. C., and D. M. O’Brien (1998), Estimating downward clear sky long-wave irradiance at the surface from screen temperature and precipitable water, Q. J. R. Meteorol. Soc., 124, 1391– 1401.
Formetta G., Antonello A., Franceschi S., David O., Rigon R., "The informatics of the hydrological modelling system JGrass-NewAge" in 2012 International Congress on Environmental Modelling and Software Managing Resources of a Limited Planet, Sixth Biennial Meeting, Manno, Swizerland: iEMSs, 2012.Atti di: 6th 2012 International Congress on
Environmental Modelling and Software Managing Resources of a Limited Planet, Leipzig, Germany, 1-5 July 2012
H.V. Gupta, H. Kling, K.K. Yilmaz, and G.F. Martinez. Decomposition of the mean squared error and nse performance criteria: Implications for improving hydrological modelling.Journal of Hydrology, 377(1-2):80{91, 2009.
Idso, S. B. (1981), A set of equations for full spectrum and 8 to 14 mm and 10.5 to 12.5 mm thermal radiation from cloudless skies, Water Resour. Res., 17, 295– 304.
Idso, S. B., and R. D. Jackson (1969), Thermal radiation from the atmosphere, J. Geophys. Res., 74, 5397– 5403.
Konzelmann T, Van De Wal RSW, Greuell W, Bintanja R, Henneken EAC, Abe-Ouchi A. 1994. Parameterization of global and longwave incoming radiation for the Greenland Ice Sheet. Global and Planetary Change 9: 143–164
Prata, A. J. (1996), A new long-wave formula for estimating downward clear-sky radiation at the surface, Q. J.R. Meteorol. Soc., 122, 1127–1151.
Swinbank, W. C. (1963), Long-wave radiation from clear skies, Q. J. R. Meteorol. Soc., 89, 339–348.
Unsworth, M. H., and J. L. Monteith (1975), Long-wave radiation at the ground, Q. J. R. Meteorol. Soc., 101,13–24.
L.E. Hay, G.H. Leavesley, M.P. Clark, S.L. Markstrom, R.J. Viger, and M. Umemoto.Step wise, multiple objective calibration of a hydrologic model for a snowmelt dominated basin1. JAWRA Journal of the American Water Resources Association, 42(4):877{890,2006.
Fig 1: Methodology: raster maps and
meteorological data are the inputs of the LWRB
package. After the automatic calibration of the
parameters, it gives the total, DL and UL longwave
radiation.
Geomorphologic model setup
Meteorological Interpolation tools
Energy balance
Evapotranspiration
Runoff production and Snow Melt
Channel routing
Automatic calibration
Input
Raster maps (Dem, Sky View Factor)
Meteorological Forcing Data (Ta, H, Ts,c)
NewAge-LWRB
Model parameters (X,Y,Z,a,b)
Output
Time series or raster maps of LWRB
(total, DL and UL)
Component
Name
Formulation Reference
Angstrom ε clear = X-Y! 10-Ze
Angstrom [1918]
Brunt’s ε clear = X+Y! e
0.5
Brunt’s [1932]
Swinbank ε clear = X !10-13
!Ta
6
Swinbank [1963]
Idso and
Jackson
ε clear = 1-X !exp (-Y!10
-4
(273-Ta)
2
) Idso and Jackson
[1969]
Brutsaert ε clear = X !(e/Ta)
1/7
Brutsaert [1975]
Idso ε clear = X+Y ! 10-4
!e! exp(1500/Ta) Idso [1981]
Monteith
and
Unsworth
ε clear = (X+Y !σ! Ta
4
) Monteith and
Unsworth [1990]
Konzelmann ε clear = X+Y !(e/Ta)1/8
Konzelmann et al
[1994]
Prata ε clear = [1-(X+w)!exp(-(Y+Z! w)1/2
] Prata [1996]
Dilley and
O'brien
ε clear = X+Y!(Ta/273.16)
6
+Z!(w/25)0.5 Dilley and O'brien
[1998]
uDig-Jgrasstools-Horton Machine
GEOSTATISTIC
Kriging
DETERMNISTIC
IDW,JAMI
SHORTWAVE (SWRB)
Iqbal+Corripio model
Decomposition models
LONGWAVE(LWRB)
Brutsaert model with
different parameterizations
Penmam-Monteith Priestley-Taylor Fao-Etp-model
Hymod model Duffy model Snowmelt and SWE model
Cuencas
LUCA Particle swarm Dream
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10
KGE
Models
Station 24
KGE opt
KGE classic
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10
KGE
Models
Station 75
KGE opt
KGE classic
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10
KGE
Models
Station 129
KGE opt
KGE classic