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Contract No. DE-AC36-08GO28308

Conference Paper

NREL/CP-5D00-75911

September 2020

Progress on the National Solar 

Radiation Data Base (NSRDB): 

A New DNI Computation

Preprint

Yu Xie,1 Manajit Sengupta,1 Yangang Liu,2 Hai Long,1 

and Aron Habte1 

1 National Renewable Energy Laboratory 2 Brookhaven National Laboratory 

Presented at the 47th IEEE Photovoltaic Specialists Conference (PVSC-47) 

June 15–August 21, 2020 
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Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

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Conference Paper

NREL/CP-5D00-75911

September 2020

Progress on the National Solar 

Radiation Data Base (NSRDB): 

A New DNI Computation

Preprint

Yu Xie,1 Manajit Sengupta,1 Yangang Liu,2 Hai Long,1 

and Aron Habte1 

1 National Renewable Energy Laboratory 2 Brookhaven National Laboratory 

Suggested Citation 

Xie, Yu, Manajit Sengupta, Yangang Liu, Hai Long, and Aron Habte. 2020. Progress on 

the National Solar Radiation Data Base (NSRDB): A New DNI Computation: Preprint. 

Golden, CO: National Renewable Energy Laboratory. NREL/CP-5D00-75911. 

https://www.nrel.gov/docs/fy20osti/75911.pdf. 

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provided by U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Solar Energy 

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1 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 

Progress on the National Solar Radiation Data Base 

(NSRDB): A new DNI computation

Yu Xie 

National Renewable Energy 

Laboratory 

Golden, CO, USA

yu.xie@nrel.gov 

Manajit Sengupta

National Renewable Energy 

Laboratory 

Golden, CO, USA

manajit.sengupta@nrel.gov 

Yangang Liu

Brookhaven National 

Laboratory

Upton, NY, USA

lyg@bnl.gov

Hai Long

National Renewable Energy 

Laboratory 

Golden, CO, USA

hai.long@nrel.gov

Aron Habte

National Renewable Energy 

Laboratory 

Golden, CO, USA

aron.habte@nrel.gov

Abstract—This study introduces a new technique to compute 

direct normal irradiance (DNI) for improving the National 

Solar Radiation Data Base (NSRDB). A finite-surface 

integration algorithm is developed to compute solar radiation in 

differential solid angles and efficiently infer its contribution to a 

surface perpendicular to the solar direction. A lookup table of 

cloud bi-directional transmittance distribution function (BTDF) 

is developed by use of the discrete ordinates radiative transfer 

(DISORT) model for possible solar and observing directions and 

various cloud optical and microphysical properties. In each 

solar incident direction, DNI is given by the cloud BTDFs from 

approximately 200 differential solid angles. The simulated DNI 

is calibrated and evaluated using surface observations at the 

National Renewable Energy Laboratory’s (NREL’s) Solar 

Energy Research Laboratory (SRRL) and the Atmospheric 

Radiation Measurement (ARM) Southern Great Plains (SGP) 

facility.

Keywords—solar radiation, DNI, NSRDB, radiance. 

I. INTRODUCTION 

Direct Normal Irradiance (DNI) representing solar 

radiation received by a surface that is perpendicular to the 

straight line from the direction of the sun is often used to 

assess the solar resource and is particularly crucial in 

evaluating the performance of concentrating solar power 

(CSP) systems [1]. Numerous radiative transfer models 

assume that DNI is related to a narrow beam covering only 

the solar disk where the Lambert-Bouguer law is used in the 

numerical computation of DNI [2]. However, DNI is often 

interpreted differently in solar observation by pyrheliometers 

[3-6]. For example, the ISO-9488 standard defines direct 

irradiance by “the quotient of the radiant flux on a given plane 

receiver surface received from a small solid angle centered 

on the sun’s disk to the area of that surface.” This indicates 

that the circumsolar diffuse radiation might affect the 

accuracy of DNI computed by the radiative transfer models. 

This study seeks to improve the National Renewable Energy 

Laboratory’s (NREL’s) National Solar Radiation Data Base 

(NSRDB) by computing circumsolar radiation and 

understanding its impact on the numerical simulation of DNI 

in various cloud conditions.

II. COMPUTATION OF DNI

Figure 1 shows a flowchart of the algorithm to compute 

DNI for clear- and cloudy-sky conditions. For clear-sky 

conditions, the atmospheric and land surface 

propertiese.g., the amount of precipitable water vapor 

(PWV), the concentration of carbon dioxide, surface 

pressure, and land surface albedofrom surface or satellitebased observations are used by a radiative transfer model 

designed for cloudless scenarios to calculate DNI [7]. For 

cloudy-sky conditions, the direct radiation is computed by 

considering three components: the direct radiation in an 

infinite-narrow beam, the first-order diffuse radiation in the 

circumsolar region, and multiple reflection between cloud 

and land surface that falls into the circumsolar region. 

Figure 1 Flowchart of the computation of DNI in clear- and 

cloudy-sky conditions.

Figure 2 demonstrates the three components of the DNI. 

According to the Beer-Bouguer-Lambert law, the direct 

radiation in the infinite-narrow beam can be given by

DNId0 = F0Tdd

clrexp �− τ

μ0

� (1) 
2 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 

where F0 is the extraterrestrial solar radiation, τ is the cloud 

optical thickness, and Tdd

clr is the transmittance of direct 

radiation in the clear atmosphere. 

Figure 2 The direct radiation in an infinite-narrow beam 

(upper), the first order diffuse radiation in the circumsolar 

region (middle), and multiple reflection between cloud and 

land surface that falls into the circumsolar region (lower). 

The first-order diffuse radiation in the circumsolar region can 

be computed by

DNId1 = F0Tdd

clrTddcld (2)

where TTdddd

cccc is the cloud transmittance of the first order direct 

radiation that can be computed by the 64-stream discrete 

ordinates radiative transfer (DISORT) model [8]. The 

multiple reflection between cloud and land surface that falls 

into the circumsolar region can be given as follows:

DNId2 = 1

μ0

� I2cosθsinθdθdφ

Ω(θ0)

(3)

where μμ00 is the cosine value of the solar zenith angle, ΩΩ(θθ00)

is the solid angle related to the circumsolar region, θθ00 is the 

solar zenith angle, θθ is zenith angle, and φφ is the azimuth 

angle. II22 is the radiance of the solar radiation related to the 

multiple reflection between the cloud and land surface. In this 

study, II22 is computed by the Fast All-sky Radiation Model 

for Solar applications (FARMS) [9-13] by assuming isotropic 

reflection of solar radiation by the land surfaces [14]. 

III. CONCLUSIONS

Figure 3 NREL SRRL and ARM SGP sites that are used to 

validate the new DNI model. 

To validate the new DNI model, we employed long-term 

data from surface-based measurements at National Renewable 

Energy Laboratory’s (NREL’s) Solar Radiation Research 

Laboratory (SRRL) (Fig. 3). The 1-minute resolution cloud 

fraction, surface pressure, surface albedo, and solar zenith 

angle from September 1, 2008 to January 27, 2019 are utilized 

to compute DNI. With the assumption of a homogenous water 

cloud layer when the observed cloud fraction is greater than 

0.95, the cloud optical thickness is estimated by the GHI 

measurement and FARMS using a variety of cloud optical 

thicknesses. The observations from January 2, 1998 to 

December 31, 2014 at the Atmospheric Radiation 

Measurement (ARM) Southern Great Plains (SGP) facility are 

also used in the validation (Fig. 3). Our results show that the 

percentage error (PE) for water clouds has been reduced from 

74.98% to 22.93% by using the new DNI model. For ice 

clouds, the PE has been reduced from 78.85% to 44.15%. The 

new DNI model will be used in the future updates of the 

NSRDB.

ACKNOWLEDGEMENTS 

This work was authored in part by the National Renewable 

Energy Laboratory, operated by the Alliance for Sustainable 

Energy, LLC, for the U.S. Department of Energy Office

(DOE) under Contract No. DE-AC36-08GO28308. Funding 
3 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 

provided by U.S. Department of Energy Office of Energy 

Efficiency and Renewable Energy Solar Energy 

Technologies Office. The Brookhaven National Laboratory 

is operated by the Brookhaven Science Associates, LLC 

(BSA), for the U.S. Department of Energy under Contract 

No. DE-SC0012704. The views expressed in the article do 

not necessarily represent the views of the Department of 

Energy or the U.S. Government. The U.S. Government 

retains and the publisher, by accepting the article for 

publication, acknowledges that the U.S. Government retains 

a nonexclusive, paid-up, irrevocable, worldwide license to 

publish or reproduce the published form of this work, or 

allow others to do so, for U.S. Government purposes.

This research was performed using computational 

resources sponsored by the Department of Energy's Office of 

Energy Efficiency and Renewable Energy and located at the 

National Renewable Energy Laboratory. 

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