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ANALYSIS OF UV-B IRRADIANCES MEASURED SIMULTANEOUSLY AT TWO STATIONS IN CZECHIA

(the dependence of the solar UV-B radiation
on total ozone and solar zenith angle)

Martin Dubrovsky

              www.ufa.cas.cz/dub/dub.htm

Institute of Atmospheric Physics,
Husova 456, 50008 Hradec Kralove, Czechia

to be presented in
a) General Assembly of European Geophysical Society, 20-24 April 1998, Nice, France
b) European Conference on Atmospheric UV Radiation (ECUV), 29 June - 2 Jul, Helsinki, Finland

acknowledgement: sponsored by the Grant Agency of the Czech Republic

Contents:

• introduction
• • • figure: location of the stations
• database
• analysis of data
• • Comparison of the measurements obtained at the two locations; effect of the altitude is quantified.
  • • figure: time series of daily sums of UVB irradiances at the two locations
    • figure: (Hradec Kralove vs. Milesovka)  vs.  Solar Zenith Angle
  • Radiation Amplification Factor and its dependence on solar zenith angle is derived from the data.
  • • figure: Radiation Amplification Factor vs Solar Zenith Angle
  • The statistical model relating UV-B irradiance with solar zenith angle and total ozone is built.
  • • figure: comparison of models
    • figure: accuracy of the model
  • UV-B climatology is reconstructed with use of the statistical model and the total ozone climatology. Changes in UV-B radiation due to recent changes of total ozone are estimated.
  • • figure: the model-based mean annual cycle of midday clear-sky erythemal UVB irradiance for various levels of total ozone concentration
    • figure: daily cycle of UV-B radiation for June 21 and various levels of total ozone
  • total ozone climatology (Hradec Kralove, 1962-1997; Dobson data)
  • • figure: The mean annual cycle of total ozone
    • figure: Time series (locally weighted moving average with t¹3 window)
      of monthly and annual means of total ozone
    • figure: Trend in total ozone
• references

Introduction:

The contribution was prepared within the frame of the joint grant project (1996-98) proposed and solved by Solar and Ozone Observatory of Czech Hydrometeorological Institute and Institute of Atmospheric Physics. The aims of the project include: (i) monitoring of UV-B radiation on a territory of the Czech Republic, (ii) operational information service, and (iii) short range forecasting of UV-B radiation intensity.

The contribution gives the results of analysis of the series of 10minute sums of erythemal UV-B irradiances measured simultaneously during August 1996 - June 1997 at two locations:

• Hradec Kralove (50.1° N 15.5° E; 278 m a.s.l., representative of lowlands; operated by SOO), and
• Milesovka (50.33°N 13.56° E; 827 m a.s.l., representative of highlands; operated by IAP).

Following items will be discussed:

• Comparison of the measurements obtained at the two locations; effect of the altitude is quantified
• Radiation Amplification Factor and its dependence on solar zenith angle is derived from the data.
• The statistical model relating UV-B irradiance with solar zenith angle and total ozone is built.
• Using the statistical model, the UV-B climatology is reconstructed with use of the total ozone climatology. Changes in UV-B radiation due to recent changes of total ozone are estimated.

Database:

• UVB_(obs)........10 minute sums of erythemally weighted UVB irradiance measured by RB-biometer at the two locations
• TO...... total ozone measured by Dobson spectrophotometer in Hradec Kralove
• SUN ........ hourly sunshine measured at the two locations (HK and MIL) (this characteristic was used to identify clear-sky terms)
• SZA.....solar zenith angle (the angle bound by observer-sun join and local vertical).

The database comprises measurements from period 1996/08/28 - 1997/06/25. The database includes 4986 clear-sky observations made in HK and 3240 observations made in Milesovka (the difference between the two numbers is mainly due to the drop-outs in Milesovka observatory).

erythemally weighted UVB radiation:

UVB = INTEGRAL w_ery(L)*I(L)*dL

where

L................. wavelength
w_ery(L) ....... erythemal weighting function (action spectrum)
I(L) ......... monochromatic irradiance

Comparison of UV-B irradiance measured at the two locations

time series of daily sums of UVB irradiances at the two locations

(1 MED = 210 J/m²)

Legend:

• sun > 3/10: days with sunshine duration exceeding 30% of possible sunshine
• 1/10 < sun <3/10: days with sunshine duration being between 10 and 30%
• sun < 1/10: days with sunshine duration lower than 10%

Notice:

• the fit between the two stations improves with increasing sunshine duration (quite logical, isn't it?)
• the fit characteristic 2(MIL-HK)/(MIL+HK) exhibits no trend

(Hradec Kralove vs. Milesovka)  vs.  Solar Zenith Angle

Legend:

• measured: the ratio of UVB irradiances measured at the two stations
• adjusted: the UVB irradiances in Milesovka were adjusted for the different latitude (using the statistical model)

Notice:

• attributing the difference between the two stations to the altitude effect, we find that UVB irradiance increases by about 7% per 1km

Radiation Amplification Factor
and its dependence on solar zenith angle

The dependence of UV-B (UVB) on total ozone uses to be expressed with use of the Radiation Amplification Factor (RAF):

UVB* /UVB*₀ = (TO /TO₀)^-RAF

which implies

d(ln UVB*) = -RAF. d(ln TO)

where UVB* = UVB/C_D is UVB irradiance adjusted for an effect of varying Sun-Earth distance (C_D = 1.00011 + 0.34221*cos(y) + 0.00128*sin(y) + 0.000719*cos(2y) + 0.000077*sin(2y), where y = 2*PI*[(J-1)/365] and J is a Julian date [Burrows et al., 1994]).

To determine RAF and its dependence on solar zenith angle, bi-linear regression analysis was applied within five 10-degree intervals of SZA on clear-sky observations. In this analysis, lnUVB* was used as a dependent variable and lnTO and SZA as independent variables.

Radiation Amplification Factor vs Solar Zenith Angle:

Radiation Amplification Factor was derived from 10min sums of erythemal UV-B radiation. The bars represent the mean and standard error of RAF.

Notice:

• the standard error of RAF is lower in Hradec Kralove than in Milesovka.

Statistical model

The model relating erythemal UVB with solar zenith angle and total ozone is assumed in form:

UVB_(SZA,TO) = UVB*_(SZA) x C_D x (TO /TO₀)^-RAF

where UVB*_(SZA) is parametrised in a following way:

UVB*_(SZA) = cos(SZA)^a  x exp{b + c.m + d.m ²}

where m = 1/cos(SZA) is an airmass. This implies:

lnUVB*_(SZA) = a ln[cos(SZA)]  + b + c.m + d.m ²

using RAF=1.06 (Hradec Kralove) and 1.11 (Milesovka), coefficients a, b, c and d were derermined by linear regression analysis from a previous equation: Hradec Kralove: a = 2.696056, b = 5.474571, c = -0.09888, d = 0.040392; Milesovka: a = 1.610082, b = 6.3914608, c = -1.134713, d = 0.1547409. The models are displayed in a following figure.

comparison of UV-B models

please note that:

• the values relate to TO = 339 D.U. and the mean Sun-Earth distance (i.e., C_D=1),
• the models were calibrated only for 25<SZA<75

Legend:

• HK(data): running (n = 50) means of UVB*
• CHMI: CHMI's model based on Brewer data
• HK(model): model for Hradec Kralove, based on present data
• MIL(model): model for Milesovka, based on present data
• HK/MIL: the ratio of the two models (Hradec Kralove vs. Milesovka)
• MIL/CHMI: the ratio of the two models (Hradec Kralove vs CHMI)

notice:

• the statistical model perfectly fits data
• present model gives higher values (by 4.5-9% within 25<SZA<70; marked by blue circles) than CHMI's model (note that the CHMI's model was developed using different source of data and from different period)
• the model for Milesovka gives higher values (by 2.5-6.5%; marked by green triangles) compared to Hradec Kralove. This may be attributed to the altitude effect (about 8% per 1km).

accurracy of the model:

Legend:

• thick lines represent reduction of root mean square error (RR) related to the knowledge of the total ozone:
  RR = 1 -RMSE(SZA,O3)/RMSE(SZA)
  where
  RMSE(SZA,O3) = s(UVB_(obs) - UVB_(SZA,O3))
  RMSE(SZA) = s(UVB_(obs) - UVB_(SZA))
  UVB_(SZA) = UVB*_(SZA) x C_D
• lines with circles represent mean relative error of the UVB models:
  s(UVB_(obs) - UVB_(SZA,O3)) / UVB_(SZA,O3)
• HK = Hradec Kralove
  MIL = Milesovka

notice:

• the mean relative error of the statistical model increases with increasing SZA and is about 10% on average
• the statistcal model better performs for HK data (may be again explained by dropouts in Milesovka and, surely, by much longer experience with radiation measurements in HK)
• the knowledge of total ozone only slightly (!) improves quality of the statistical model for low solar zenith angle
• it is assumed that the accuracy of the model might be improved by incorporating turbidity and vertical profile of ozone

reconstruction of UVB climatology
&
changes in UV-B radiation due to recent changes of total ozone

Although the UV-B radiation is not measured sufficiently long time to construct a reliable UVB climatology of the Czech Republic, we may estimate the desirable climatological characteristics for clear-sky conditions with use of the statistical model and total ozone climatology:

The model-based mean annual cycle of midday clear-sky erythemal UVB irradiance for various levels of total ozone concentration:

Legend:

• O3=a±s: total ozone = avg ±std
• O3=a±2s: total ozone = avg ± 2*std
• O3=a±3s: total ozone = avg ± 3*std
• O3=a(62-90): total ozone = average from 1962-1990
• O3=a(91-97): total ozone = average from 1991-1997
• SZA (noon): the midday solar zenith angle
  
  

notice:

• the maximum UVB irradiances occur at the break of June and July (the delay behind the summer solstice is due to the annual cycle of total ozone (see the figure))
• during low total ozone episodes (TO < avg-2*std), the expected UVB irradiance may exceed the mean annual maximum within relatively long period (May-20 to August-06) [if TO = avg-3*std, the period is May-04 to August-14]. However, even during extremely low ozone episodes in late winter and early spring (February to April) UVB irradiance cannot exceed "normal" summer UVB irradiances. In reality, the values of UVB during these "ozone hole" periods is not higher than the UVB irradiances in normal ozone conditions one month later.
• comparing 1991-1997 vs. 1962-1990: Total ozone decreased in 90's with respect to 1962-1990. The mean annual maximum based on 1962-1990 period (June 30) is thus exceeded in 1991-97 by about 5%, and the mean annual cycle based on 1991-1997 period is about 1 and 1/2 months (June-07 to July-22) above the 1962-1990 maximum.

Daily cycle of UV-B radiation for June 21 and various levels of total ozone

Legend:

• O3=a±s: total ozone = avg ±std
• O3=a±2s: total ozone = avg ± 2*std
• O3=a±3s: total ozone = avg ± 3*std
• O3=a(62-90): total ozone = average from 1962-1990
• O3=a(91-97): total ozone = average from 1991-1997

total ozone climatology
(based on Dobson data measured in Hradec Kralove)

the mean annual cycle of total ozone (Kalvova and Dubrovsky, 1995)

Legend:

• a±s: total ozone = the mean annual cycle of avg(TO) ±std(TO) (based on 1962-1990 data)
• a±3s: total ozone = the mean annual cycle of avg(TO) ± 3*std(TO) (based on 1962-1990 daily means of total ozone)
• 1991-97: mean annual cycle of daily means of total ozone in 1991-1997
• 1996 and 1997: series of daily means of total ozone in 1996 and 1997
• min62-90: the minima of daily means experienced in period 1962-1990
• min62-97: the minima of daily means experienced in period 1962-1997

Time series (locally weighted moving average with t+/-3 window)
of monthly and annual means of total ozone

trend in total ozone

References

• BURROWS W.R., VALLÉE M., WARDLE D.I., KERR J.B. WILSON L.J., TARASICK D.W., 1994: The Canadian operational procedure for forecasting total ozone and UV radiation. Met.Appl. 1, 247-265.
• Dubrovsky M. and Kalvova J., 1996: The daily total ozone: the mean annual cycle and correlation with meteorological parameters. Presented at the XVIII Quadrennial Ozone Symposium, L'Aquila, 12-21 September, 1996. The proceedings was to be published in 1997.
• Kalvova J. and Dubrovsky M., 1995: Assessments of the limits between which daily average values of total ozone can normally vary. [in Czech with English abstract and many figures with English captions] Meteorological Bulletin, 48, 9-17