In this work 10 algorithms for estimating downwelling longwave
atmospheric radiation (

The

Longwave radiation is an important component of the radiation balance on
earth and it affects many phenomena, such as evapotranspiration, snowmelt

SM performances have been assessed in many studies by comparing measured and
modelled

However, none of the above studies have developed a method to systematically estimate site-specific model parameters for location where measurements are not available using basic site characteristics.

This paper introduces the LongWave Radiation Balance package (LWRB) of the
JGrass-NewAGE modelling system

The SMs for

The LWRB component of JGrass-NewAge and the flowchart to model longwave radiation.

The formulation presented in Eq. (3) was proposed by

Ten SMs from the literature have been implemented for the computation of

Clear-sky emissivity formulations:

The models presented in Table

Model parameter values as presented in their literature formulation.

The formulation of the

It is well known that surface soil temperature measurements are only
available at a few measurement sites; therefore, under the hypothesis that
the difference between soil and air temperatures is not too big, it is
possible to simulate

The LWRB package (see the flowchart in Fig.

Sections 2.1 and 2.2, respectively, present the calibration and the verification procedure. Moreover, a model sensitivity analysis procedure is presented in Sect. 2.3 and a multi-regression model to relate the optimal parameter set and easily available meteorological data is proposed in Sect. 2.4.

Model calibration estimates the site-specific parameters of

Soil emissivity for surface types

The calibration procedure for

The theoretical solar radiation at the top of the atmosphere (

The clearness index,

Clear-sky and cloud-cover hours are detected by a threshold on the clearness
index (equal to 0.6), providing two subsets of measured

The parameters

The parameters

The calibration procedure provides the optimal set of parameters at a given location for each of the 10 models.

As well as parameter calibration, we carry out a model parameter sensitivity analysis and we provide a linear regression model relating a set of site-specific optimal parameters to mean air temperature, relative humidity, precipitation, and altitude.

As presented in previous applications

The KGE (Eq.

For each

we start with the optimal parameter set, computed by the optimization process for the selected model;

all parameters are kept constant and equal to the optimal parameter set, except for the parameter under analysis;

1000 random values of the analysed parameter are picked from a uniform
distribution centered on the optimal value with width equal to

1000 values of KGE are computed by comparing the model outputs with measured time series.

The calibration procedure previously presented to estimate the site-specific
parameters for

Test site locations in the USA.

To test and calibrate the LWRB SMs we use 24 meteorological stations of the
AmeriFlux Network (

We have chosen 24 sites that are representative of most of the contiguous USA
and span a wide climatic range, going from the arid climate of Arizona, where
the average air temperature is 16

Some general and climatic characteristics of the sites used for calibration:
elevation is the site elevation above sea level,

When implementing the 10

Figure

Results of the clear-sky simulation for four literature models using data from Howland Forest (Maine).

KGE and RMSE values for each clear-sky simulation using literature
formulations, grouped by classes of latitude and longitude. Only values of
KGE above 0.5 are shown. Only values of RMSE below 100 W m

The calibration procedure greatly improves the performances of all 10 SMs.
Optimized model parameters for each model are reported in the Supplement
(Table S1). Figure

KGE (best is 1) and RMSE (best is 0) values for each optimized formulation in clear-sky conditions, grouped by classes of latitude and longitude. Only values of KGE above 0.5 are shown.

Figure

KGE and RMSE values for each model in all-sky conditions with the optimized parameters; results are grouped by classes of latitude and longitude. Only values of KGE above 0.5 are shown.

Results of the model parameters' sensitivity analysis. The variation of the model performances due to a variation of one of the optimal parameters and assuming constant the others is presented as a boxplot. The procedure is repeated for each model and the blue line represents the smooth line passing through the boxplot medians.

The results of the model sensitivity analysis are summarized in
Fig.

Comparison between model performances obtained with regression and classic parameters: the KGE values shown are those above 0.3 and results are grouped by latitude classes.

A multivariate linear regression model was estimated to relate the
site-specific parameters

The performances of the

The cross validation results for all

In general, the use of parameters estimated with the regression model gives a
good estimation of

Comparison between model performances obtained with regression and classic parameters: the KGE values shown are those above 0.3 and results are grouped by longitude classes.

Figure

Boxplots of the KGE values obtained by comparing modelled upwelling longwave radiation, computed with different temperatures (soil surface temperature – SKIN, air temperature – AIR, and soil temperature – SOIL), against measured data. Results are grouped by seasons.

The best fit between measured and simulated

The use soil temperature at 4 cm depth provides the least accurate results
for our simulations, with an all-season average KGE of 0.46. In particular,
the use of soil temperature at 4 cm depth during the winter is not able to
capture the dynamics of

This paper presents the LWRB package, a new modelling component integrated
into the JGrass-NewAge system to model upwelling and downwelling longwave
radiation. It includes 10 parameterizations for the computation of

The LWRB is tested against measured

The main achievements of this work include (i) a broad assessment of the
classic

The integration of the package into JGrass-NewAge will allow users to build
complex modelling solutions for various hydrological scopes. In fact, future
work will include the link of the LWRB package to the existing components of
JGrass-NewAge to investigate

The LWRB package has been implemented according to the object-oriented
paradigm, making it flexible and expendable for future improvements and
maintenance. Thanks to the Gradle Build tool, an open-source automation
system, and Travis CI, a continuous integration service used to build and
test software projects, code is tagged for any release and our workflow is
traceable. For the present paper we used code version v.0.9. Versions
till 0.94 are also available in the repository. Researchers interested in
replicating or extending our results are invited to download our codes at

Instructions for using the code can be found at

Regression of parameters was performed in R and is available at

The authors are grateful to the AmeriFlux research community for providing the high-quality public datasets. In particular, we want to thank the principal investigators of each site: Shirley Kurc Papuga (AZ), Tilden P. Meyers (AZ), Russ Scott (AZ), Tom Kolb (AZ), Sonia Wharton (CA), Dennis D. Baldocchi (CA), Jordan G. Barr (FL), Vic C. Engel (FL), Jose D. Fuentes (FL), Joseph C. Zieman (FL), David Y. Hollinger (ME), Joe McFadden (MN), John M. Baker (MN), Timothy J. Griffis (MN), Lianhong Gu (MO), Kenneth L. Clark (NJ), Dave Billesbach (OK), James A. Bradford (OK), Margaret S. Torn (OK), James L. Heilman (TX), Ken Bible (WA), and Sonia Wharton (WA). The authors thank the CLIMAWARE project, of the University of Trent (Italy), and the GLOBAQUA project, which have supported their research. The authors would like to thank the editor and the unknown reviewers for their comments that helped improve the quality of the manuscript. Edited by: B. Schaefli Reviewed by: two anonymous referees