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					Forecasting the UV index for
                                 Document Reference: UFOS/TN/001
          UFOS:                  Date              : 30/08/2000
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    Model overview and
       methodology




  Forecasting the UV index for UFOS:
   Model overview and methodology




     Author: Bertrand Théodore, ACRI-ST

             August 30th, 2000




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                            Model overview and
                               methodology



                                                               Table of Contents

1       INTRODUCTION................................................................................................................................... 4

2       RADIATIVE TRANSFER ...................................................................................................................... 5
    GAS ABSORPTION MODEL.............................................................................................................................. 5
    EXTRATERRESTRIAL SOURCE SPECTRA .......................................................................................................... 6
    STANDARD ATMOSPHERIC MODELS ............................................................................................................... 6
    STANDARD AEROSOL MODELS ....................................................................................................................... 7
    SPECTRAL RESOLUTION ................................................................................................................................. 7
    SURFACE ALBEDO .......................................................................................................................................... 8
3       ACTION SPECTRA ............................................................................................................................... 9

4       A NEURAL NETWORK TO APPROXIMATE THE RADIATIVE TRANSFER ............................. 10

5       FORECASTING THE TOTAL OZONE CONTENT.......................................................................... 11
    INITIALISATION ........................................................................................................................................... 11
    ADVECTION MODEL .................................................................................................................................... 11
    WIND FIELD: THE NOGAPS MODEL ............................................................................................................ 12
6       INCORPORATION OF CLOUDS EFFECTS ..................................................................................... 12

7       INCORPORATION OF AEROSOLS .................................................................................................. 12

8       ALBEDO............................................................................................................................................... 14

9       TOPOGRAPHY.................................................................................................................................... 15

10          SYSTEM CONSIDERATIONS ........................................................................................................ 16
     PRODUCTS................................................................................................................................................... 16
     SPATIAL AND TEMPORAL EXTENT ................................................................................................................. 16
11          REFERENCES.................................................................................................................................. 18




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                                                                 List of Figures

FIGURE 1: VERTICAL PROFILE OF O3, H2O AND TEMPERATURE CORRESPONDING TO MID-LATITUDES SUMMER
    CONDITIONS USED IN THE RADIATIVE TRANSFER MODEL. ............................................................................. 6
FIGURE 2: IMPACT OF THE AEROSOL LOADING IN THE BOUNDARY LAYER (EXPRESSED BY THE ATMOSPHERIC
    VISIBILITY. ................................................................................................................................................ 7
FIGURE 3: UV INDEX AS A FUNCTION OF THE SPECTRAL RESOLUTION (LEFT FIGURE IN WAVELENGTH AND RIGHT
    FIGURE IN WAVENUMBER) OF THE RADIATIVE TRANSFER MODEL.................................................................. 8
FIGURE 4: IMPACT OF THE ALBEDO ON THE UV INDEX FOR THREE DIFFERENT ZENITH ANGLES.............................. 8
FIGURE 5: ACTION SPECTRA FOR ERYTHEMA INDUCTION, SKIN CARCINOGENESIS FOR HUMAN (SCUPH), DNA
    DAMAGE AND PLANT DAMAGE ( FROM WHO, 1994)..................................................................................... 9
FIGURE 5: PREDICTED UV INDEX AS A FUNCTION OF THE EXPECTED ONE. .......................................................... 10
FIGURE 6: BOUNDARY LAYER AEROSOLS OPTICAL THICKNESS OVER THE MEDITERRANEAN BASIN (FROM TEGEN ET
    AL., 1997)................................................................................................................................................ 13
FIGURE 7: ALBEDO MAP OVER THE MEDITERRANEAN BASIN AREA (AVERAGED OVER 0.5X0.5 DEGREES). ............ 14
FIGURE 8: ALTITUDE MAP OVER THE MEDITERRANEAN BASIN AREA (IN METRES, AVERAGED OVER 0.5X0.5
    DEGREES). ............................................................................................................................................... 15




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1 Introduction

This document describes the model used in the UFOS project to compute the UV indices, that
is a weighted integral between 280 and 400 nm of the solar irradiance reaching the ground,
over the Earth’s surface.

The UV irradiance on a specific location depends on many variable, the most significant ones
being absorption by ozone and attenuation (primarily due to backscattering) by clouds and
aerosol over that particular point. Physical characteristics such as the local hour, the altitude
and the season also have an impact on the energy received at the ground level.

There is a wealth of so-called “radiative transfer” codes available for the rigorous
computation of the light propagation through the atmosphere, provided that the detailed
optical properties of the atmosphere, required as inputs, are known. It is important to note that
such information is, in general, not routinely available, especially in forecast mode. The
computation of the UV index has thus to rely on standard meteorological information.

Schwander et al. (1997) have performed a thorough investigation in order to assay the relative
importance of the various parameters required in the computation of the UV irradiance. They
claimed that the main contributor to the UV irradiance uncertainty comes first from
uncertainties in the total ozone value, followed by errors in the aerosol optical depth and
aerosol optical properties (absorption and spectral course of the optical depth). On the other
hand, they pointed out that “modelling of the UV irradiance with a high accuracy is possible
without the provision of actual vertical profiles of atmospheric constituents”. They
established that, using what they called a “minimum subset of input variables” (namely O3
and SO2 total content, assumed ground albedo and aerosol optical depth estimated from the
atmospheric visibility at 550 nm), the erythema-weighted UV index can be estimated with an
accuracy in the range 10-15 %, depending on the solar zenith angle. Note that their study does
not include the effect of clouds.

These results led us to state that, for UFOS:

q   Total column ozone is forecasted using a model initialised with daily analyses of GOME
    soundings and driven by forecasts of the winds;
q   The vertical profiles of the atmospheric constituents are taken from climatologies. The
    vertical profile of ozone is adjusted such that the total column matches the predicted
    value;
q   In the absence of systematic global measurements of the aerosols optical depth, a
    climatology is used;
q   The ground albedo is estimated from the soils coverage;
q   The UV index is computed in clear sky conditions and subsequently corrected for altitude
    and clouds; no attempt is made to compute the radiative transfer through clouds for the
    lack of routinely available information about their optical properties.




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2 Radiative Transfer

Methods used for solving the radiative transfer divide into three categories:

q   Multiple scattering spectral models (hereafter referred as to MSS models) that include a
    rigorous treatment of the physics involved in the phenomenon, to the expense of a high
    numerical cost;
q   Fast spectral models in which some kind of parameterisation (analytical simplification of
    the radiative transfer equation) lightens the computational burden;
q   Empirical models that are direct parameterisations, using analytical functions, of the
    measured UV index.

A comparison between several models belonging to these classes has been performed by
Koepke et al. (1998). They showed that, although much more computationally expensive, the
MSS models are more flexible than fast and empirical models. Noteworthy is the fact that the
codes belonging to this category all give similar results.

We have thus chosen such a MSS model, namely the SBDART code from the Earth Science
Group of the University of California at Santa Barbara, for its immediate availability. It is
based on a classical discrete ordinate radiative transfer module DISORT developed by
Stamnes et al. (1988) and have been thoroughly validated. Hereafter are presented some of its
features.


                                  Gas Absorption Model

SBDART relies on low resolution band models developed for the LOWTRAN 7 atmospheric
transmission code. These models provide the clear sky atmospheric transmission and include
the effects of all radiatively active molecular species found in the earth's atmosphere. The
models were derived from detailed line-by-line calculations which were degraded to 20 cm-1
resolution for use in LOWTRAN.

Because these band models represent rather large wavelength bins, the transmission functions
do not necessarily follow Beer’s law; i.e., the fractional transmission through a slab of
material depends not only on the slab thickness but also on the amount of material penetrated
before entering the slab. In order to allow these transmission functions to be used with
DISORT (which assumes Beer’s law behaviour), the band models are approximated with a
three term exponential fit (Wiscomb and Evans, 1977).




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                           Extraterrestrial Source Spectra

SBDART may be run with any of three extraterrestrial solar spectrum models. We used the
LOWTRAN-7 solar spectrum (Thekeakara, 1974). This model is based on measurements
between 300 and 610nm.



                            Standard Atmospheric Models

SBDART includes six standard atmospheric which are intended to model the following
typical climatic conditions: tropical, mid-latitude summer, mid-latitude winter, sub-arctic
summer, sub-arctic winter and US62. These model atmospheres have been widely used in the
atmospheric research community and provide standard vertical profiles of pressure,
temperature, water vapour and ozone density (see an example for mid-latitudes summer
conditions on the figure below). The concentration of trace gases such as CO2 or CH4 are
assumed to make up a fixed fraction of the total particle density.




 Figure 1: vertical profile of O3, H2O and temperature corresponding to mid-latitudes
                summer conditions used in the radiative transfer model.




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                                Standard Aerosol Models

SBDART can compute the radiative effects of several common boundary layer and upper
atmosphere aerosol types.

In the boundary layer, the user can select either rural, urban, or maritime aerosols. These
models differ from one another in the way their scattering efficiency, single scattering albedo
and asymmetry factors vary with wavelength. The impact of the aerosol loading in the
boundary layer (expressed by the atmospheric visibility) is shown on the figure below.




     Figure 2: impact of the aerosol loading in the boundary layer (expressed by the
                                 atmospheric visibility.

In the upper atmosphere up to 5 aerosol layers can be specified, with radiative characteristics
that model fresh and aged volcanic, meteoric and tropospheric background aerosols.




                                    Spectral resolution

Tests have been performed in order to assess the influence of the spectral resolution on the
value of the UV index. The spectral step size of the computation can be specified in
SBDART in term of constant increment of wavelength or wavenumber. It turned out that the
constant wavenumber increments lead to more stable results as the resolution is reduced. We
chose a spectral resolution of 20cm-1 appeared to be optimal (figure below) as it corresponds
to the resolution of LOWTRAN whose results are used in the radiative transfer.


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Figure 3: UV index as a function of the spectral resolution (left figure in wavelength and
             right figure in wavenumber) of the radiative transfer model.


                                       Surface albedo

The value of the UV index for three value of the zenith angle has been plotted as a function of
the surface albedo. It is apparent that the variation may be assumed to be linear in the range 0,
0.2, typical of the UV albedoes that are generally much lower than their visible counterparts.




    Figure 4: Impact of the albedo on the UV index for three different zenith angles.


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3 Action spectra

The sensitivity of organisms to UV radiation is a function of wavelength. This is represented
by a so-called “action spectrum” that is the reciprocal of the radiant exposure required to
produce a given effect at each wavelength. Below are presented the action spectra we use in
UFOS, normalised to 1 at 250 nm.




     Figure 5: action spectra for erythema induction, skin carcinogenesis for human
             (SCUPh), DNA damage and plant damage (from WHO, 1994).


The integration over wavelength of the product of the spectral irradiance with an action
spectrum yields the so-called instantaneous dose rate:

                               dose rate = ∫ W ( λ ) ⋅ B ( λ ) ⋅ d λ

The weighting function corresponding to the sensitivity of Caucasian skin to erythema-
causing radiations (labelled as “Erythema on the above plot) has been adopted as a standard
by the Commission Internationale de l’Eclairage.




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4 A Neural Network to Approximate the Radiative Transfer

As alluded before, the computation of the UV index using a full (multiple scattering) radiative
transfer model is computationally expensive such that it is not realistic to use it for routine
operations. In order to alleviate that problem, we trained a neural network such that it gives
directly the value of the UVI that would have been obtained using the whole radiative transfer
algorithm.

To do so, we used the NNFIT (Neural Network FITting) code developed at Laval University,
Quebec. NNFIT is a non-linear regression program based on multi-layered neural network
models that allows user-friendly development and application of neural empirical relations
between input and output variables.

For each of the UV indices computed in UFOS (UVA, UVB, DNA, erythema, SCUP-h and
plant) a neural network has been set up with four input neurones (fed with, respectively, the
solar zenith angle, the O3 column density, the aerosols optical thickness and the albedo), one
hidden layer consisting in nine nodes and one output (the UV index).

A database of about 5000 cases was constructed from randomly generated values for each of
the four variables, yielding a fair coverage of the state space. 70 % of the database was used
for the supervised learning while the other 30 % serves the generalisation which prevents the
network to “learn by heart”.

Below is plotted the predicted erythema-weighted UV index as a function of the expected one.
If the network were perfect, all the points would lie on the diagonal. It can be seen that the
network performs fairly well.




             Figure 6: predicted UV index as a function of the expected one.


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5 Forecasting the Total Ozone Content

The forecast of the ozone content relies on the 2D advection of the total column using a wind
field at a single pressure level, a method already used and validated at KNMI (Levelt et al.,
1996). Ozone may indeed be considered as a tracer in the upper troposphere/lower
stratosphere region: its distribution is thus mainly driven by the wind field. Levelt et al.
further argued that the total ozone variability is dominated by a thin layer around the
tropopause where ozone exhibits the maximum temporal variability; they found that using
only the 200 hPa winds for the transport of the ozone column yields fairly good forecasts.


                                         Initialisation

The model is initialised with analyses of GOME soundings of the total ozone, provided daily
by the KNMI in the frame of the ESA’s Data User Program.

The GOME level 4 archive files contain the assimilated total ozone columns at 12h GMT
each day. The spatial sampling is 1 degree in latitude and 1.25 degree in longitude and the
effective resolution (width of the auto-correlation function of the distribution of ozone values
around a latitude circle) is 800 km. All measurements are given in Dobson units and are
integers with 3 significant figures. One file is about 162 Ko.


                                      Advection Model

Horizontal transport is performed with a semi-lagrangian algorithm. These algorithm are
widely used (Williamson and Rash, 1989) as they exhibit useful properties:

q   monotonicity;
q   small numerical diffusion;
q   possible use of large time steps without loss of stability and precision;
q   The drawback is that mass-conservation is not insured.

The algorithm we use was developed for use in the UIUC chemical-transport model (Zubov et
al., 1999). It is run with a resolution of 0.5 degrees, that is about 50 km in mid-latitudes. In
order to lessen the importance of the mass conservation problem, this algorithm combines
high-order (Hermite cubic) interpolation and low-order (linear), strictly monotonic,
interpolation. The advantage of this approach is that the correction (“fixing”) of the Hermite
cubic interpolation by the low-order interpolation is performed only in regions having strong
horizontal gradients of species concentration, where the high-order interpolation contributes
predominantly to the mass-conservation error.




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                             Wind Field: the NOGAPS Model

The wind fields are taken from the NOGAPS model outputs that are distributed through the
MEL web interface. The NOGAPS (Navy Operational Global Atmospheric Prediction
System) forecast model is a global model that is spectral in the horizontal and energy-
conserving finite difference (sigma coordinate) in the vertical. The model top pressure is set at
1 hPa; however, the first velocity and temperature level is approximately 5 hPa. There are 24
vertical levels with approximately 6 levels below 850 hPa. The horizontal truncation is 159
that is about 0.75 degrees on a gaussian grid.

Analyses at 0h and 12h GMT as well as associated three days forecasts of the zonal and
meridional components of the wind field at 200 hPa and of the fractional cloudiness are
downloaded about 2h30 after the synoptic times. One “tar” file (containing the analysis and
the forecasts) represents about 3Mo.


6 Incorporation of Clouds Effects

Cloudiness is the most important contributors to the short time and spatial scales variability in
the UV irradiance reaching the ground. Although radiative transfer computation through
clouds is theoretically possible, the lack of information about their type, altitude and
composition, fixing their optical properties, prevents to do so in routine operations. Frederick
and Steele (1995) have investigated to what extent standard meteorological information may
be used to account for clouds effects in the computation of the UV irradiance. If only the
fractional cloud cover f is available, as in our case, they recommend to correct the clear sky
irradiance using the linear relationship 1-0.56f. They claimed, however, that such a simple
fixer may be greatly improved if the cloud ceiling altitude and the horizontal visibility are
known.


7 Incorporation of Aerosols

The optical thickness of the boundary layers aerosols is derived from the climatology from
Tegen et al. (1997), shown on the figure below. It is estimated from the global distribution of
aerosol loading resulting from models for soil dust sulfate, sea salt, and carbonaceous aerosol.




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Figure 7: boundary layer aerosols optical thickness over the Mediterranean basin (from
                                  Tegen et al., 1997).




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8 Albedo

Albedo is derived from a characterization of the land cover. The latter is available from the
U.S. Geological Survey's (USGS) Earth Resources Observation System (EROS) Data Center,
the University of Nebraska-Lincoln (UNL) and the Joint Research Centre of the European
Commission as a 1-km resolution global land cover characteristics data derived from
Advanced Very High Resolution Radiometer (AVHRR). The regions are composed of
homogeneous land cover associations (for example, similar floristic and physiognomic
characteristics) which exhibit distinctive phenology (that is, onset, peak, and seasonal
duration of greenness)

The mapping between land cover and albedo uses the following table:

                              Urban and built up land       10 %
                              Cropland/Grassland            2%
                              Forest                        3%
                              Water                         14 %
                              Wetland                       3%
                              Barren/Sparsely vegetated     2%
                              Snow/Ice                      50 %

The resulting dataset is illustrated on the figure below.




    Figure 8: albedo map over the Mediterranean basin area (averaged over 0.5x0.5
                                     degrees).



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9 Topography

Elevations were taken from the USGS’s Global 30-Arc-Second Elevation Data Set
(GTOPO30). This data set covers a range of latitude from 90 degrees north to 90 degrees
south and a range of longitude from 180 degrees west to 180 degrees east. The horizontal grid
spacing is 30 arc-seconds (0.008333 degrees or approximately 1 kilometre). The vertical units
represent elevation in meters above mean sea level, ranging from -407 to 8,752 meters. Small
islands in the ocean less than approximately 1 square kilometre are not represented.

Altitudes were averaged over a grid with a resolution of 0.5 degrees in latitude and longitude
that matches the resolution of the grid on which the UV indices computation is performed. On
figure 8 is illustrated our dataset.




  Figure 9: altitude map over the Mediterranean basin area (in metres, averaged over
                                   0.5x0.5 degrees).




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10 System considerations

                                           Products

In the current version, UFOS computes six clear-sky and six cloud-corrected “UV indices”
i.e. instantaneous dose rate:
q UVA (integral of the irradiance between 315 and 400 nm);
q UVB (integral of the irradiance between 280 and 315 nm);
q CIE erythemal;
q DNA;
q SCUPh;
q Plant.
The action spectra used to compute the last four values were presented hereabove.

In addition, the following auxiliary products, that is data that were used in the calculation, are
stored:
q Total ozone column;
q Total aerosols optical thickness;
q Fractional cloud cover;
q Albedo;
q Altitude.




                                Spatial and temporal extent

All the products, i.e. UV indices and auxiliary products, are given on a grid covering a region
that encompasses the Mediterranean sea that is extending from –20 to 40 degrees in longitude
and from 26.5 to 47.5 degrees in latitude with a resolution of 0.5 degrees in longitude and 0.5
degrees in latitude (this represent 121× 44 points).

Three days forecasts of the total ozone field are performed by the advection model using a
time resolution of 6 hours and a spatial resolution of 0.5 × 0.5 degrees over the whole Earth.
These fields are kept internally and are not available to the user.

Forecasts of the UV indices are computed with 6 neural networks every 1 hour. These fields
are then corrected to account for the cloud cover and the altitude as explained above. The
ozone content as well as the cloud cover at each time step are obtained by linearly
interpolating between adjacent times. The maximum values of the UVIs for each day are
stored along with the values corresponding to the analysis (at t = 0 ). Thus 4 fields of 12
indices are stored at each run of the model. Conversely, the auxiliary products are stored only
once at t = 0 .

On the figure below is schematised the system architecture.




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        Figure 9: UFOS system architecture.




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11 References

[1] Bodeker G. E., and R. L. McKenzie, 1996. An algorithm for inferring surface UV
    irradiance including cloud effects. J. Appl. Meteor. 34, 1860-1877.
[2] Frederick J. E., and H. D. Steele, 1995. The transmission of sunlight through cloudy skies:
    an analysis based on standard meteorological information. J. Appl. Meteor. 34, 2755-
    2761.
[3] Koepke P. et al., 1998. Comparison of models used for UV index calculations.
    Photochem. Photobiol. 67, 657-662.
[4] Levelt P. F., M. A. F. Allaart, and H. M. Kelder, 1996. On the assimilation of total ozone
    satellite data. Ann. Geophys. 14, 1111-1118.
[5] Schwander H., P. Koepke, and A. Ruggaber, 1997. Uncertainties in modelled UV
    irradiances due to a limited accuracy and availability of input data. J. Geophys. Res. 102,
    9419-9429.
[6] Stamnes K., S. C. Tsay, W. Wiscombe, and K. Jayaweera, 1988. Numerically stable
    algorithm for discrete-ordinate method radiative transfer in multiple scattering and
    emitting layered media. Appl. Opt. 27, 2502-2509.
[7] Tegen I. et al., 1997. Contribution of different aerosol species to the global aerosol
    extinction optical thickness: estimates from model results. J. Geophys. Res 102, 23895-
    23915.
[8] Thekeakara, M.P., 1974. Extra-Terrestrial solar spectrum, 3000-6100 A at 1 A intervals,
    Appl. Opt. 13, 518-522.
[9] World Health Organization, 1994. Ultraviolet radiation; an authoritative scientific review
    of environmental and health effects of UV, with reference to global ozone layer depletion.
    Environment Health Criteria 160, WHO, Geneva.
[10] Wiscomb, W.J., and J.W. Evans, 1977. Exponential-Sum Fitting of Radiative
    Transmission Functions, J. Comp. Phys. 24, 416-444.
[11] Williamson, D. L., and P. J. Rasch, 1989. Two-dimensional semi-Lagrangian transport
    with sharp-preserving interpolation. Mon. Weather Rev., 117, 102-129.
[12] Zubov V. A., E. V. Rozanov, and M. E. Schlesinger, 1999. Hybrid scheme for 3-
    dimensional advective transport. Mon. Weather Rev. 127, 1335-1346.




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