Introduction
Concentrated solar power (CSP) projects require accurate assessment of the
available direct beam resource. Ground measurements have to be combined with
satellite-derived data for this assessment. These ground measurements can be
obtained by solar trackers and pyrheliometers or by rotating shadowband
irradiometers (RSIs). Due to their lower susceptibility to soiling, RSIs have
an important advantage over thermopile pyrheliometers during long-term
deployment in remote and inaccessible sites, where daily cleaning of the
instrument's aperture is not possible (Geuder and Quaschning, 2006; Pape et
al., 2009; Maxwell et al., 1999). RSIs are also advantageous in terms of
installation and maintenance costs and the typically achieved data
availability.
RSIs consist of a pyranometer and a shadowband that rotates once per
minute around the pyranometer such that the sensor is shaded for some time.
Examples for RSIs can be seen in Fig. 1. When the shadowband is in its
resting position, the global horizontal irradiance (GHI) is measured. Diffuse
horizontal irradiance (DHI) is measured during the rotation and direct normal
irradiance (DNI) is calculated using GHI, DHI and the solar zenith angle. RSIs are
often called RSRs or RSPs, depending on the instrument manufacturer. Instead
of irradiometer, radiometer or pyranometer appear in these names. The
notation RSI refers to all instruments that measure irradiance by use of a
rotating shadowband. There are two types of RSIs: RSIs with continuous and
discontinuous rotation. The operational principal of RSIs with continuous
rotation is explained in the following. At the beginning of the rotation,
the shadowband is below the pyranometer, in its resting position. The
rotation occurs with a constant angular velocity and takes approximately 1
to 2 s. During the rotation, the irradiance is measured with a high
and constant sampling rate (e.g. 1 kHz). This measurement is analyzed in
order to derive GHI and DHI for the time of the rotation. In this paper only RSIs
with continuous rotation of the shadowband are discussed. Such RSIs need a
pyranometer with a fast response time (≪ 1 ms, e.g.
10 µs). Thus, thermal sensors as described in ISO 9060 (1990) cannot be
used. Instead, semiconductor sensors are used, e.g. the Si-pyranometer
LI-200SA (LI-COR, 2004).
Rotating shadowband irradiometers. Left: RSR2 (irradiance Inc.),
center: RSP4G (Reichert GmbH), right: Twin-RSI (CSP Services GmbH) (Wilbert
et al., 2015).
RSIs with discontinuous rotation do not use a continuous and fast rotation,
but a discontinuous stepwise rotation. Instead of measuring the complete
signal during the rotation, only four points of it are measured (Harrison
et al., 1994). First, the GHI is measured while the shadowband is in the
resting position. Then the shadowband rotates from the resting position
towards the position where it nearly shades the pyranometer, stops and a
measurement is taken (e.g. for 1 s). Then it continues rotating towards the position in which the shadow lies centered on the pyranometer
and another measurement is taken. The last point is measured in a position
in which the shadow just passed the pyranometer. RSIs with discontinuous
rotation require a much more accurate adjustment of the instrument's azimuth
orientation than RSIs with continuous rotation, as well as an exact time
adjustment. Such RSIs will not be discussed here.
So far, RSIs with continuous rotation use the LI-COR LI-200SA pyranometer.
This photodiode instrument experiences systematic errors due to cosine and
temperature effects and its non-uniform spectral responsivity. A number of
correction functions can be employed to reduce these errors significantly.
The combination of the publications (King and Myers, 1997; King et al.,
1998; Augustyn et al., 2004; Vignola, 2006) provide a set of
functions which use the ambient temperature, solar zenith angle, air mass,
GHI and DHI as input parameters. Geuder et al. (2008) introduced a separate set
of correction functions which uses an additional spectral parameter
determined from GHI, DHI, and DNI. An improved version of these corrections has been
analyzed in Geuder et al. (2016).
A thorough calibration of RSIs with application of the correction functions
is required for the utmost quality of measurements. The calibration
procedures of thermopile pyranometers and pyrheliometers are well documented
in standards such as ISO 9059 (1990), ISO 9846 (1993) and ISO 9847 (1992). These standards
are not directly applicable to RSIs due to their inherent characteristics,
especially because of the spectral selectivity of the Si-pyranometers used
in RSIs. The inhomogeneous spectral response of results in the problem that
the calibration for a given atmospheric condition and air mass might not
work for a different condition with a corresponding different spectrum.
Hence, specific calibration procedures for RSIs were developed by the
German Aerospace Center (DLR), for example. In this paper DLR's calibration methods shall
be called DLR2008 and VigKing (a detailed description follows in Sect. 2).
They include significantly longer measuring periods and require measurements
from a wider range of meteorological conditions than previously mentioned
standards. The longer calibration durations ensure that the calibration is
not derived only from extreme spectral conditions. In further deviation from
the ISO standards for thermopile sensors, the RSI calibration methods by DLR
assign more than one calibration factor for each instrument, since multiple
components of solar irradiance with differing spectral composition and
sensor responsivity are determined.
Parameter list.
Symbol
Description
Units
θ
temperature
∘C
ΔDNI
conservative estimate of relative DNI uncertainty
%
ΔSoil
uncertainty due to pyrheliometer soiling
%
Π
ratio of moving average to the long-term mean value
%
A
set of all timestamps of available data
date/hour/minute
CFD
DHI calibration factor in DLR2008 calibration
–
CFd
DHI calibration factor in VigKing calibration
–
CFG
GHI calibration factor in DLR2008 calibration
–
CFg
GHI calibration factor in VigKing calibration
–
CFn
DNI calibration factor in VigKing calibration
–
DHI
diffuse horizontal irradiance
W m-2
DNI
direct normal irradiance
W m-2
GHI
global horizontal irradiance
W m-2
L
long-term mean value of R
–
M
moving average of R
–
m
number of timestamps within one series of data
–
n
number of timestamps within a moving interval
–
R
ratio of the reference irradiance to the corrected and calibrated
–
irradiance measured by the RSI
SZA
solar zenith angle
∘
T
duration of the moving interval representing the calibration duration
days
t
timestamp for a 10 min interval
date/hour/minute
These RSI calibration methods have been applied at the Plataforma Solar de
Almería (PSA) (latitude 37.0909∘ N, longitude
-2.3581∘ E, altitude 500 m a.m.s.l., semi-arid
climate) for a number of years. However, some details are still under
investigation to increase the reliability. A thorough assessment of the
necessary calibration duration and seasonal influences on calibration
results has now been carried out with several years of measurements from
five RSIs. This paper outlines two RSI calibration procedures developed by
DLR and presents the site-specific findings with regard to calibration
durations and seasonal influences at PSA. It should be mentioned that only
calibrations from one site (PSA) are evaluated and the conclusions are
therefore partially site specific. However, although meteorological
parameters may differ from site to site, the effect of fluctuating
calibration results in accordance to seasonal influences is a general
problem in outdoor calibration of Si-Pyranometers. Similar results are
expected at sites of similar latitude and climate conditions. The site
dependence of the performance is discussed in Geuder et al. (2016).
Evaluated RSI calibration methods
This paper discusses two calibration methods applied at PSA. In addition to
the calibration, RSIs require the application of aforementioned correction
functions in order to reduce the photodiode sensors' systematic error. Each
of the calibration methods corresponds to a different set of correction
functions. Therefore, the following differentiates between the calibration
method corresponding to functional corrections by Geuder et al. (2008;
called DLR2008) and the calibration method corresponding to functional
corrections by King, Myers, Augustyn and Vignola as published in King and
Myers (1997), King et al. (1998), Augustyn et al. (2004), Vignola (2006)
(called VigKing). Some functions in the latter set have been published in
varying versions. The working set used in VigKing calibrations was
summarized in Wilbert et al. (2015).
Both methods assign individual calibration factors to different irradiance
components in addition to the LI-200SA Silicon-Pyranometer manufacturer's
(LI-COR) calibration factor. The RSI is compared to a reference direct
normal irradiance (DNIRef) and a reference diffuse horizontal irradiance
(DHIRef) that are measured with a ISO 9060 first class pyrheliometer and a
secondary standard pyranometer (shaded with a shadowball), respectively.
More specifically, Kipp&Zonen CH1 or CHP1 pyrheliometers and CMP21 or
CMP11 are used depending on the time interval under evaluation. The
reference global horizontal irradiance (GHIRef) is calculated via
GHIRef=DNIRef×cosSZA+DHIRef
from both reference instruments since this yields higher accuracy than GHI
measurement by a pyranometer (see ISO 9060, 1990). Nonetheless, a second
pyranometer that measures GHI directly is used to control the reference
measurements as a redundancy check.
Subscript list.
Subscript
Description
acc
accepted data points
amb
ambient
cal
calibration
cor
functionally corrected RSI value
DHI
pertaining to DHI
DNI
pertaining to DNI
d
at 12:00 pm
GHI
pertaining to GHI
max
maximum
Ref
reference for calibration
RSI
functionally corrected and calibrated RSI value
raw
uncorrected value measured by RSI
Data collection at PSA usually takes place continuously over the course of
30 to 120 days while the test RSI is positioned within less than 10 m
from the reference instruments. Tables 1 and 2 provide the reader with a reference for parameters and subscripts used in equations. However, since RSIs are mostly employed in
the context of CSP, only measurements under CSP operating conditions are
included in the calculation of calibration factors. These conditions are
specified later in detail. Due to the manifold environmental and operational
influences which can occur during this time span, the raw data need to be
screened and manually reviewed for errors and temporary system failures. The
calculation of the calibration factors is based on minimizing the root mean
square deviation (RMSD) but differs for both methods.
Another approach to RSI calibration was published in Kern (2010) which only
compares GHI measurements from the photodiode to a reference and thus replaces
the sensor manufacturer's calibration factor. However, this method is not
subject of this paper.
Calibration method DLR2008
This calibration method assigns two calibration factors: CFG for GHI and CFD for DHI
which are applied in accordance to Eqs. (2) to (4). Since both GHI and DHI have
different spectral compositions, the sensor's responsivity differs among the
two. The typical difference in responsivity is incorporated into the
correction functions and hence the correction refers to the responsivity for
the two components averaged over the group of instruments used for the
development of the correction functions. However, the difference in
responsivity for GHI and DHI is specific to each individual sensor as deviations
of the spectral response between different instruments occur. Thus, better
results are achieved by using separate calibration factors (Geuder et al.,
2008). Because DNI is the desired measurand, CFG is optimized for determination of
the DNI. The improved version presented in Geuder et al. (2016) allows a
separate adjustment of calibration constants for GHI and DNI.
After calibration the final irradiance values measured by the RSI
(GHIRSI, DHIRSI and DNIRSI) are obtained as
described in the following. GHIRSI is obtained by multiplying the
calibration factor CFG to the functionally corrected global horizontal
irradiance (GHIcor):
GHIRSI=CFG×GHIcor.
The calculation of the functionally corrected and calibrated DHI differentiates
between two cases. While the uncorrected DNI is at 2 W m-2 or above the
equation
DHIRSI=CFD×DHIcor
is used. If the uncorrected DNI is lower than 2 W m-2, the calculation
uses GHI and reads as
DHIRSI=CFD×GHIcor.
The reason is that at such low DHI values, usually there is little or no DNI, and
thus DHI is equal to GHI; therefore the GHI value measured each second is more accurate
than the DHI value derived from the measurement during the brief rotation.
The corrected and calibrated DNI, DNIcor is determined from the corrected
and calibrated GHIRSI, DHIRSI and the solar zenith angle SZA as
DNIRSI=GHIRSI-DHIRSIcos(SZA).
The calibration process itself starts with data collection and documentation
as follows. First, GHIRef, DHIRef and DNIRef are sampled every
second and recorded as 1 min average values as well as the ambient
pressure and temperature. Then the RSI values for GHI, DHI and DNI are averaged and
recorded once per minute. The number of samples used per average value
differs between the irradiance components since DHI can only be measured while
the sensor is shaded (see sampling rates in Table 3). Furthermore, the
sampling rate before calculation of 1 min values differs for RSR2
(irradiance Inc.), RSP-4G (Reichert GmbH) and Twin-RSI (CSP Services GmbH).
In RSP-4G and Twin-RSI sensors, the sensor temperature is also recorded. A
comprehensive summary of how the irradiance components are derived from the
photodiode's signal can be found in Wilbert et al. (2015).
The next step is the monitoring of the measurements. In order to identify
and resolve operational problems, the recorded data of all instruments are
scrutinized at least once per weekday by manually reviewing the reference
and test data. Furthermore, the instruments are cleaned and inspected every
weekday in situ for anomalies. The exact time of each cleaning event is
documented. The redundant GHI measurement is used to control the operation of
the reference instruments. Operational errors are documented in the
calibration database. All relevant events concerning the measurement station
and in the vicinity (e.g. construction works, maintenance of nearby
instruments) are documented.
RSR2, RSP4G and Twin-RSI sampling rates (Wilbert et al., 2015).
Rotation frequency
GHI
DHI
DNI
Twin RSI
1/ (30 s) alternating for both sensors
1/ s
Shadowband correction averaged with previous value
Calculated from GHI, DHI and solar position as 1 min average with correction for DHI drift
RSR2
at least 1/ (30 s) up to 1/ (5 s) if 20 W m-2 change in GHI
1/ (5 s)
Averaged for each rotation
Averaged for each rotation
RSP4G
1/ (60 s)
1/ s
Calculated once per minute as average of two rotations
Calculated every second from 1 s GHI samples. Averaged every 60 s
The data treatment includes the following steps. For each data channel
10 min mean values are calculated from the recorded 1 min averages:
performing the calibration in 10 min time intervals reduces the signal
deviation between reference and RSI at intermediate skies which results from
the distance between the sensors and moving clouds. Then a screening
algorithm performs a quality check of all recorded channels as recently
presented in Geuder et al. (2015). Among other tests, the quality check tests
and marks if measured values are physically possible, if their fluctuation
(or lack of it) is realistic and if the data points have been manually
flagged/commented during the measuring period. Furthermore, a soiling
correction algorithm is applied to DNIRef in accordance to the documented
cleaning events following the method from Geuder and Quaschning (2006).
Then, the LI-COR calibration factor CFLicor is applied to the RSI data.
Afterwards, the not yet calibrated and still uncorrected RSI time series,
reference time series and time series of the signal deviations are checked
for consistency by an expert. If one of the six irradiances seems to be
unreliable, it is removed from the calibration data set. The manual
discarding of data by expert intervention only excludes typically less than
1 % of the calibration data set. In the improbable case that erroneous
data are not excluded or that valid data are excluded, only small effects on
the calibration results occur.
For RSI without temperature sensor (e.g. RSR2) the sensor temperature is
estimated using the following Eq. (6) from Wilbert et al. (2015) based on
GHI and ambient temperature θamb:
θRSI=θamb+(-4.883×10-6×GHIraw2+0.00953×GHIraw-0.5).
Another estimation algorithm substitutes missing pressure measurements in
all RSIs using the barometric formula. This is used in calculation of the
apparent solar angle including refraction and is in particular required at low
solar elevations.
Then the GHIRef is calculated by using the apparent sun height at the
middle of each 10 min interval and the irradiance data are compared
again. First, the deviation of GHIraw, DHIraw and DNIraw (RSI data
with applied CFLicor) and the reference data are checked for plausibility
by comparison against the reference irradiance components in scatterplots
for each component. Implausible data are removed. Irradiance data which have
been flagged by the screening algorithm as potentially erroneous are marked in the scatterplots and
excluded. In a second check the deviation
of RSI data from the reference data before and after application of the
functional corrections (specific to the calibration method, here DLR2008)
are compared to each other. Criteria for implausible data include high
deviation between reference DNI (pyrheliometer) and calculated DNI from the
reference pyranometers (> 8 % for SZA < 75∘;
> 15 % for greater SZAs) and high deviations between test and
reference instruments (> 25 %). Erroneous data are marked for
exclusion and a comment is saved in the database.
The central step is the calculation of calibration factors. The solar
elevation angle, GHIRef and DHIRef as well as their deviation from the
functionally corrected but not yet calibrated RSI measurements GHIcor and
DHIcor are filtered for their respective calibration limits (Table 4). The
calibration limits define the acceptable range of irradiance and solar
elevation angle for calibration as specified in Table 4. Then the DHI
calibration factor CFD is determined by minimization of the root mean square
deviation (RMSD) of DHIRSI from DHIRef through variation of CFD.
Thereafter, while ignoring the previous GHI and DHI data screening, the solar
elevation angle, DNIRef, and its deviation from the corrected RSI
measurement, DNIcor, is screened for its calibration limits (Table 4). With CFD calibration factor applied, the screened data are used to determine the
calibration factor CFG for GHI by minimization of the RMSD of DNIRSI from
DNIRef by variation of CFG.
Calibration limits (Geuder et al., 2011).
Reference DNI (W m-2)
> 300
Reference GHI (W m-2)
> 10
Reference DHI (W m-2)
> 10
Solar elevation angle (∘)
> 5
Max deviation of corrected RSI from reference (%)
±25
Finally, the calibration results are manually reviewed. The deviation of
corrected RSI data from the reference before and after calibration is
compared. Bias, standard deviation and RMSD of the corrected and calibrated
RSI data from the reference are calculated and serve as indicators for the
quality of the calibration. If further erroneous data are found, they can be
marked for exclusion, and the calculation of the calibration constants is
repeated.
The calibration procedure for the improved version (Geuder et al., 2016) is
similar to the described one with the exception that CFG is optimized for GHI
(instead of DNI). Here, two further calibration constants for DNI are introduced
and fitted to the DNI dependent on its intensity after several filtering steps.
This method, however, is not analyzed here.
Calibration method VigKing
VigKing determines three separate calibration factors CFg, CFd and CFn for GHI, DHI and
DNI respectively (Geuder et al., 2011). Each calibration factor is optimized
for RMSD for the irradiance component it is applied to.
The calibration factors are applied in accordance to Eqs. (7) to (10).
The functionally corrected and calibrated GHI (GHIRSI) is
obtained by multiplying the functionally corrected GHIcor by the GHI
calibration factor CFg:
GHIRSI=CFg×GHIcor.
The DHI correction is given with the functionally corrected GHIcor as a
parameter. After calibration, the functionally corrected and calibrated
DHIRSI is calculated along the corrections from Vignola (2006) with
GHIRSI as GHI input.
If GHIRSI≤ 865.2 W m-2, the DNI is calculated along Eq. (8) as
DHIRSI=CFd×[DHIraw+GHIRSI×(-9.1×10-11×GHIRSI3+2.3978×10-7×GHIRSI2-2.31329234×10-4×GHIRSI+0.11067578794)].
Equation (9) is used, if GHIRSI > 865.2 W m-2:
DHIRSI=CFd×[DHIraw+GHIRSI×(0.0359-5.54×10-6×GHIRSI)].
The corrected and calibrated DNIRSI is determined with the DNI calibration
factor CFn as
DNIRSI=CFn×GHIRSI-DHIRSIcos(SZA).
Note that the application of three calibration factors results in combinations of DNI, GHI and DHI that are not completely self-consistent. The calibration factor
CFn is usually between 1.005 and 0.995 and hence the self-inconsistency is not
very pronounced. The average of the absolute amount of 1 - CFn for 76 calibrations carried out at PSA between September 2013 and August 2015 is
0.0057.
In all aspects other than the correction functions and the assignment of a
third calibration factor, the VigKing calibration method is identical to the
method DLR2008 presented in Sect. 2.1. Contrary to the account given in
Geuder et al. (2011) in today's practice, the same calibration limits (Table 4) are used in both calibration methods. The determination of the three
calibration constants is done as follows.
GHIRef and DHIRef as well as their deviation from the corrected but not
yet calibrated RSI measurements GHIcor and DHIcor are filtered for their
respective calibration limits and solar elevation angle (Table 4). The
screened data are then used to determine the GHI calibration factor CFg by
minimization of the RMSD of the corrected and calibrated GHIRSI from
GHIRef. Thereafter, the previous data screening for calibration limits is
repeated with applied CFg before the screened data are used to determine the
DHI calibration factor CFd by minimization of the RMSD of the corrected and
calibrated DHIRSI from DHIRef. Then, with applied CFg and CFd, the corrected
but not yet calibrated RSI measurement DNIcor is screened for calibration
limits (Table 4). Finally the screened data are used to determine the DNI calibration
factors CFn by minimization of the RMSD of the corrected and calibrated
DNIRSI from DNIRef.
Evaluation of RSI calibration duration and seasonal influences
A first site-specific assessment of the necessary calibration duration at
PSA has been presented in Geuder et al. (2014) in which a minimum measuring
period of 30 days was recommended based on data collected from a single
instrument. We investigated the subject further by use of a total of seven
long-term data sets ranging from 251 to 1289 day duration collected over a
period of 6.5 years from five RSI instruments (Table 5). Calibrating an
instrument with the entire available long-term measuring period is
considered the best achievable result.
Based on an application of moving averages the fluctuation of calibration
results for different calibration durations was compared to the result of a
long-term calibration over the whole period of available data. This was done
separately for each of the seven long-term data sets. The deviation of
calibration results from a long-term calibration with regard to DNI is
represented by ΠDNI as defined in the following.
First the instrument is calibrated over the entire available long-term
measuring period by either method from Sect. 2. The thereby derived
calibration factors are applied to the functionally corrected 10 min mean
values of RSI measured irradiance from the calibration period. For the
following steps the same manual and automatic data exclusions and the
application of calibration limits (Table 4) as applied during the
calibration process are kept in place. The remaining data are used to
calculate the ratio RDNI of reference to the calibrated RSI irradiance
along
RDNI(t)=DNIRef(t)DNIRSI(t).
The timestamp t indicates the 10 min interval. Thereafter, the moving
average (here: moving in steps of 24 h) of RDNI is calculated as
MDNIT,td=1n×∑tRDNI(t)witht∈td-T2,td+T2⋂Aacc,
where td represents a timestamp at noon and T is the duration of the
moving interval and thus represents the evaluated calibration duration. T is
an integer number of days. Aacc is the set of all timestamps of the
available data that were accepted after applying the exclusion parameters
from Table 4 and the manual sort out by an expert. n is the number of
timestamps which are considered for the summation. As td is always noon
(UTC + 1) of a given day we calculate only one moving average
MDNIT,td for each day.
Evaluated data sets.
Instrument
From
To
Duration
[days]
RSP-4G-08-10-1
8 Aug 2008
16 Sep 2009
404
RSP-4G-08-10-3
29 Jul 2010
7 Feb 2014
1289
RSR2-0017
9 Sep 2009
16 May 2010
251
RSR2-0018
17 May 2007
15 Oct 2008
517
RSR2-0036
12 Nov 2007
12 Aug 2008
274
RSR2-0039-1
12 Nov 2007
13 Aug 2008
292
RSR2-0039-2
1 Jan 2011
18 Jan 2012
382
Additionally, LDNI the mean of RDNI over the entire
measurement series is calculated along the equation
LDNI=1m×∑tRDNItwitht∈Aacc
where m is the number of timestamps within the set Aacc. Finally,
ΠDNI(T,td)=MDNIT,tdLDNI
is calculated as the ratio of the moving average MDNI to the mean of
RDNI over the entire calibration period represented by LDNI. The
evaluation method as described above was applied separately for both
calibration methods DLR2008 and VigKing, and its findings are discussed in
the following sections.
Evaluation results for the method DLR2008
Figure 2 displays the distribution of ΠDNI for each RSI data set
(Table 5) and for varying calibration duration in form of box plots. In the
type of box plots used in this paper the whiskers include 99.3 % of all
values in the case of normal distribution. The box itself includes 50 %
of all values with the first quartile below and the third quartile above its
edges. The horizontal line signifies the median, while the circle symbolizes
the arithmetic mean.
As expected, the whiskers of each data set get closer to zero with increased
calibration duration T since the influence of isolated extreme spectral
conditions is evened out by the greater amount of data used. Similarly, the
overall presence of outliers (exceptionally deviating calibration results)
is reduced significantly. Due to the high volatility of calibration results
for measuring periods below 14 days as seen in Fig. 2 such durations are
considered as insufficient. In comparison to all other sensors, increasing
the calibration duration from 1 to 30 days does not decrease the
interquartile ranges significantly for the RSR2-0039-1. Since the power
supply of the RSR2-0039 had to be exchanged between the measurement sets
RSR2-0039-1 and RSR2-0039-2, we assume that this defect is the reason for
the behavior.
DLR2008: distribution of ΠDNI depending on
calibration duration for seven data sets. ΠDNI represents the
deviation of calibration results from a long-term calibration for DNI.
Calibrations of 180 days duration or more on the other hand are too
time-consuming in practice, especially considering the recommended frequency
of recalibration of 2 years given in Geuder et al. (2014). Another
disadvantage of very long-term calibrations is the lag time. Therefore,
further analysis focuses on durations of 14, 30, 60, 90 and 120 days.
The ΠDNI were plotted over the time span of the long-term
calibration measuring for one RSI data set at a time as shown in Fig. 3 for
the RSP-4G-08-10-3 data set and calibration durations of T=14 days,
T=60 days, T=90 days and T=180 days. The horizontal axis represents the
date and the first day of each month is represented by vertical grid lines.
The left vertical axis displays ΠDNI while the second vertical
axis provides the daily number of usable timestamps. In this representation
each plotted data point refers to the middle timestamp of its interval
td.
The number of usable timestamps per day clearly coincides with the seasons.
This is common to all data sets (Table 5) at hand and is a clear correlation
to the daily daylight hours. Therefore, a calibration of the same duration
differs in the amount of usable data dependent on the time of the year.
In order to derive recommendations for the necessary calibration duration
for different times of the year, the ΠDNI of the seven data sets
(Table 5) was sorted by the starting month of calibration and the combined
distribution of all RSI data sets was visualized in box plots as presented in
Fig. 4. This allows choosing the required duration in dependence of the
starting time of measurements and the acceptable distribution of ΠDNI. The same was done for ΠGHI and ΠDHI in Figs. 5
and 6. Since most of the time the greater part of GHI is due to DNI in CSP
relevant regions, the seasonal course of ΠGHI (Fig. 5)
distributions displays more similarities with the seasonal course of
distributions of ΠDNI (Fig. 4) than of ΠDHI (Fig. 6).
The highest volatility is observed in ΠDHI.
DLR2008: time series of ΠDNI for varying
calibration duration for RSP-4G-08-10-3 with daily number of usable
timestamps. ΠDNI represents the deviation of calibration results
from a long-term calibration for DNI.
DLR2008: distribution of ΠDNI for T=14 days, 30 days,
60 days, 90 days and 120 days sorted by calibration starting month. ΠDNI represents the deviation of calibration results from a long-term
calibration for DNI.
Most boxes in Fig. 4 are well centered on their respective arithmetic mean.
The course of the ΠDNI reaches its maximum between November and
January and its minimum between March and May. This indicates a small
seasonal dependence of the calibration results. The longest calibration
duration of T=120 days reaches its
maximum ΠDNI in October, while a
short duration of 14 days causes its respective maximum value to be 2 months
later. This is due to the different
calibration data set and the application of the starting month for the x axis. The general observation is that the longer the calibration
duration, the closer the outcome will be to a long-term calibration. In this case, the
conditions of the long-term calibration represent the application
conditions, a long-term calibration is thus preferred. While this is true in
most cases, some exceptions can be found. In Fig. 4 for starting dates in
November and T=60 days the ΠDNI are distributed further from
zero than with any other of the evaluated durations T. This is true for all
statistical values that the box plot provides (whiskers, mean, etc.). However, a duration of T=60 days exhibits better distributions of ΠDNI than durations of 14 and 30 days for starting dates in the
following month of December (better in terms of coincidence with ΠDNI=0). For starting dates in January, the differences between
the distribution of ΠDNI for 30 and 60 days duration is
further increased. This indicates that the meteorological conditions in
November and February are generally more suitable for DLR2008 calibration
and later RSI application at PSA than in December and January.
DLR2008: distribution of ΠGHI for T=14 days, 30 days,
60 days, 90 days and 120 days sorted by calibration starting month. ΠGHI represents the deviation of calibration results from a long-term
calibration for GHI.
DLR2008: distribution of ΠDHI for T=14 days, 30 days,
60 days, 90 days and 120 days sorted by calibration starting month. ΠDHI represents the deviation of calibration results from a long-term
calibration for DHI.
Furthermore, starting dates in January produced closer coincidence between
ΠDNI and zero with a duration of T= 90 days than a
duration of T=120 days. The ΠDNI of starting dates in
February exhibited the closest coincidence with zero for durations of
T=60 days along with T=30 days. 90 days periods starting in January and
60 days periods starting in February have in common that they end in April
while the respective longer periods include all of April and a part of May.
Remarkably, the duration T=120 days generated the greatest deviation of
ΠDNI values from zero for starting dates in February. This is
owed to the inclusion of the entire period of meteorological conditions in
April and May.
DLR2008: Minimum required calibration duration in days for given
maximum of ΠDNI and starting time.
ΠDNI,max
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
±2.5 %
30
14
14
14
14
14
14
14
14
14
14
60
±2.25 %
30
14
14
14
14
14
14
14
14
14
14a
60
±2 %
60
14
14
14
30
14
14
14
14
14
90
90
±1.5 %
60
14
14
90
60
30
30
30
14
30
120
120
±1 %
90
30b
120
90
60
30
60
30
90
90
–
120
±0.75 %
90
–
–
120
90
90
90
120
–
90
–
–
lowest
90
30
120
120
120
120
120
120
120
120
120
120
a 60 days is not suitable.
b Only 60 days and 30 days are suitable.
However, out of all data visualized in Fig. 4 the ΠDNI
distributions for starting dates in May and June with T= 120 days
exhibited the smallest distance between upper and lower whiskers as well as
the closest coincidence with 0 % since the respective periods of time are
dominated by the more suitable conditions from June onward.
As shown by these examples, the rough rule that longer calibration durations
yield better results does not always apply, due to the meteorological
conditions (i.e. spectral composition of irradiance) at the time. Exceptions
to be considered are discussed in the following.
Recommendations for DLR2008 calibration duration
In consideration of the seasonal tendencies, it is recommendable to vary the
calibration duration dependent on the month in which the measurements are
commenced. This allows us to keep the monthly maximum deviation of MDNI (Eq. 12) from LDNI (Eq. 13) within a given maximum (hereafter called
ΠDNI,max) and thus creates results of closer to constant viability
while minimizing calibration duration. Table 6 provides a summary of
required minimum durations for varying ΠDNI,max. Exceptions are
marked in the table and explained in the caption. For example, even if a
constant calibration duration of T=60 days is preferred to choosing the
duration individually by month of the year, a reduction of the duration for calibrations starting in November to T=30 days
only should be considered, since for this month a duration of T=60 days exhibited the highest
ΠDNI in comparison to any other examined duration between 14 and
120 days.
The evaluation of seasonal influences was used to establish the correlation
between ΠDNI,max, calibration duration and the month in which a
calibration is commenced. Since ΠDNI represents the deviation of
individual short-term calibrations from the result of a long-term
calibration, ΠDNI,max in combination with the relative standard
uncertainty of the reference pyrheliometer (DNIRef) can be used for a
conservative estimate of calibration uncertainty:
ΔDNIcal≈ΔDNIRef2+ΔSoil2+ΠDNI,max2.
In accordance with WMO (2010) the relative uncertainty of our reference
pyrheliometer is 1.8 % (95 % confidence level). We hence assume
ΔDNIRef=0.9 % for the standard uncertainty. Additionally,
an uncertainty due to pyrheliometer soiling of ΔSoil ≈ 0.2 %
can be estimated in respect of the findings in Geuder and Quaschning (2006).
The calibration error can have a systematic component. The calibration error
of the reference instruments causes a similar calibration error for the RSI
calibration. The contribution of the soiling to the error is small due to
the maintenance efforts at PSA and the soiling correction for the reference
data. If less frequent cleaning is provided and no or insufficient soiling
corrections are applied, additional systematic errors can occur, as the
reference instruments are more sensitive to soiling than the RSIs under
calibration.
An exemplary calculation for ΠDNI,max=2.25 % results in an
estimated ΔDNIcal≈ 2.4 % of the calibration
uncertainty. It should be mentioned that this estimation includes the
uncertainty caused by the spectral response of the solid state pyranometer
that has to be expected for application at PSA after the calibration at PSA.
Also other uncertainty contributions (e.g. directional, linearity and
temperature effects) are partly included in this estimation because the bulk
of the data in a calibration periods might belong to confined ranges of
these parameters.
VigKing: Minimum required calibration duration in days for given
maximum of ΠDNI and starting time.
ΠDNI,max
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
±2.25 %
30
14
14
14
60
14
14
14
14
14
30
30
±2 %
30
14
14
60
60
14
14
14
14
14
30
30
±1.5 %
60
30
14
90
60
14
60
60
30
14
120
90
±1 %
90
60a
30a
120
90
60
120
120
90
–
–
120
±0.75 %
90a
–
–
120
90
60
–
–
120
–
–
–
lowest
90
60
30
120
120
90b
120
120
120
90
120
120
a Only this duration.
b Positioning of IQR better than 120 days.
The calibration accuracy should also be related to the required accuracy for
typical RSI applications. RSIs are usually applied for solar resource
assessment that involves the combination of ground and satellite data. The
uncertainty of the satellite data is typically much higher than the
uncertainty of the ground measurements if best practices are followed for
the measurements. An estimate of the maximal acceptable uncertainty of the
combined data set from Meyer et al. (2008) is 4.5 %. According to this
publication, the required accuracy can be reached with two satellite data
sets of moderate quality and an uncertainty of 4 % for the ground
measurements. The achieved calibration uncertainty is therefore sufficient
for the creation of these combined data sets and it is also sufficient for
other applications (e.g. the validation of forecasted irradiance data;
Schenk et al., 2015).
Recommendations for VigKing calibration duration
The duration of VigKing calibrations is evaluated in the same fashion in the
previous section for DLR2008.
In comparison to DLR2008, the VigKing method results in similar seasonal
distributions of ΠDNI. The rough rule that longer calibrations
result in less deviation from the long-term calibration is also applicable in this
case. However, some differences can be found. In Fig. 7 it is noticeable
that the VigKing produces wider interquartile ranges of ΠDNI. This
is especially true for starting dates during the time from November to
January. During this period, the distributions are exceptionally symmetrically
centered around zero but exhibit the widest range of ΠDNI values.
With calibration method VigKing (Fig. 7) the ΠDNI distributions
for starting dates in March were the closest to zero for durations of 30 days. Contrarily, in the following 2 months of April and May the
distributions of ΠDNI for a duration of T=30 days deviate
further from zero than for other durations. This observation indicates that
the meteorological conditions during April and May are not well suited for
VigKing calibrations. In the case of calibrations which start in April or
May but reach well into the months of June or July a far closer coincidence
of the ΠDNI with zero is achieved. This is caused by the more
suitable conditions from June onward. A similar tendency was observed in
DLR2008 (Fig. 4).
In DLR2008, the duration of 60 days produced the highest upper ΠDNI whiskers among calibrations starting in November (Fig. 4). This is
not true for VigKing (Fig. 7) where only T=14 days exhibits higher values
than T=60 days. On the other hand, in regard to maximum ΠDNI and interquartile range a duration of T=30 days exhibits a more
desirable distribution for this starting month than a duration of 60 days.
Measurements starting in October with 30 to 90 days duration resulted in
smaller ΠDNI than 120 days duration due to the adverse
conditions during the winter months. Considering the interquartile ranges of
ΠDNI, a duration of 90 days appears to perform best for
calibrations starting in the month of October.
VigKing: distribution of ΠDNI for T=14 days, 30 days,
60 days, 90 days and 120 days sorted by calibration starting month for
VigKing. ΠDNI represents the deviation of calibration results from
a long-term calibration in regard to DNI.
Similarly as for DLR2008 calibrations, a table has been created to choose
the calibration duration for VigKing depending on the month of the year
and the desired ΠDNI,max (Table 7).
If a constant calibration duration throughout the year is preferred, also
for VigKing a duration of T=60 days is advised as a trade-off between
producing results close to a long-term calibration and not consuming more
time than reasonable. Similarly to DLR2008 one should resort to a shorter
duration of T=30 days for calibrations starting in November. In VigKing
the same is true for calibrations starting in March. Figure 7 suggests a
deviation from a long-term calibration below 2 % for T=60 days
throughout the year.
Conclusions
The influence of the RSI calibration duration and the seasonal fluctuations
of two calibration methods at PSA were investigated. Small but noticeable
seasonal dependencies were observed. Also some fluctuations of RSI
calibration results were found that are influenced by the calibration
duration. Thus, it was possible to quantify relations which can be used to
optimize the calibration duration dependent on the time of the year in which
a calibration takes place.
Additionally, the findings allowed the identification of periods with higher
likelihood of adverse meteorological conditions (November to January and
April to May). Consequently, the duration of data acquisition for
calibrations starting during these months should generally be longer than
for calibrations starting during the rest of the year. In some cases it is
advantageous to limit the duration of calibrations starting before these
periods so that these periods are not used.
In order to apply the results of this analysis, two tables were constructed,
which allows one to choose the calibration duration for both calibration
methods depending on the month of the year in which measurements are
commenced and the maximum tolerable value of ΠDNI,max, which
represents the fluctuation of calibration results (Tables 6 and 7). For
DLR2008 a constant calibration duration of 30 days throughout the year with
the exception of calibrations starting in December (60 days) is sufficient
to keep ΠDNI,max within 2.5 %. In VigKing calibrations, the
same applies with the exception of using 60 days duration for calibrations
starting in the month of May instead of December.
The subject of calibration uncertainty was briefly discussed in this paper
and is a subject for further investigation. We found that during certain
periods, deviation of calibration results exhibits positive (November to
January) one-sided tendencies and negative (April and May) one-sided
tendencies. Further investigation is necessary to see if these seasonal
effects can be attenuated by additional or improved functional corrections.
In the future, the evaluation method used in this paper could also be
applied to the improved version of DLR2008.