Improvement of diffuse solar irradiance measurements with noncosine instruments

As a result of sky radiance anisotropy, significant errors spoil diffuse solar irradiance data obtained by means of noncosine-true instruments, which happens in spite of knowledge of the relative cosine response. To reduce these errors we recommend a method that involves an additional measurement of diffuse irradiance from a horizon band. The efficiency of the so-called double-measurement method is found to be optimum for a 25° horizon band elevation. We confirm the feasibility of the method with relevance tests that use diffuse solar spectral measurements carried out on cloudless skies by means of an UV spectroradiometer.     

Estimation of absorption and backscattering coefficients from in situ radiometric measurements: theory and validation in case II waters

A model that relates the coefficients of absorption (a) and backscattering (b(b)) to diffuse attenuation (K(d)), radiance reflectance (R(L)), and the mean cosine for downward irradiance (mu(d)) is presented. Radiance transfer simulations are used to verify the physical validity of the model for a wide range of water column conditions. Analysis of thee radiance transfer simulations suggest that absorption and backscattering can be estimated with average errors of 1% and 3%, respectively, if the value of mu(d) is known with depth. If the input data set is restricted to variables that can be derived from measurements of upward radiance (L(u)) and downward irradiance (E(d)), it is necessary to use approximate values of mu(d). Examination of three different approximation schemes for mu(d) shows that the average error for estimating a and b(b) increases to approximately 13%. We tested the model by using measurements of L(u) and E(d) collected from case II waters off the west coast of Scotland. The resulting estimates of a and b(b) were compared with independent in situ measurements of these parameters. Average errors for the data set were of the order of 10% for both absorption and backscattering.     

Asymptotic optical depths in source-free ocean waters

The depth dependence for which the downward diffuse attenuation coefficient, the upward-to-downward plane irradiance ratio, the vertically upward radiance-to-downward plane irradiance ratio, and the mean cosine of the radiance depend negligibly on the surface incident illumination have been examined. The depths at which these coefficients approach to within a specified percent of their asymptotic values depends significantly on the characteristics of the incident illumination and on the inherent optical properties of the water. This information is useful when solving inverse ocean optics problems with a method for which the radiance is assumed to be approximately in the asymptotic regime.     

Thermodynamic Radiation Thermometry Using Radiometers Calibrated for Radiance Responsivity

Using radiometry, thermodynamic temperatures can be determined by a variety of experimental techniques. Radiometers without imaging optics can be calibrated for spectral power or spectral irradiance responsivity, and radiometers with imaging optics can be calibrated for radiance responsivity. These separate approaches can have different uncertainty components with different uncertainty values. At NIST, thermodynamic radiation thermometry is performed using radiation thermometers calibrated for radiance responsivity using laser-irradiated integrating sphere sources (ISS). The radiance of the ISS is determined using Si-trap detectors whose spectral power responsivity is traceable to the electrical substitution cryogenic radiometer. The radiometric basis of the NIST approach is discussed. The uncertainty budget for the measurements as well as the characterizations to determine the component uncertainty values is listed.     

Self-shading of upwelling irradiance for an instrument with sensors on a sidearm

The self-shading measurement error of the upwelling irradiance that is due to the presence of the instrument housing of an optical spectrometer with the irradiance meter located on a sidearm was calculated with a Monte Carlo code. The dependence of the effect on the instrument dimensions, the values of real optical parameters, sea-surface roughness, and Sun zenith angle were all studied to estimate maximum errors for two possible configurations of a proposed new marine spectrophotometer.     

Radiance reflected from the ocean-atmosphere system: synthesis from individual components of the aerosol size distribution

We describe a method by which the aerosol component of the radiance at the top of the atmosphere (TOA) can be synthesized from the radiances generated by individual components of the aerosol size-refractive-index distribution. The method is exact in the single-scattering approximation. For regimes in which the single-scattering approximation is not valid, the method usually reproduces the aerosol contribution with an error ?2-3% (and only rarely >3-4%) for Sun and viewing angles as large as 80° and 70°, respectively, and for aerosol optical thicknesses as large as 0.50. In the blue, where molecular scattering makes a dominant contribution to the TOA radiance, the percent error in the synthesized total radiance is significantly less than in the synthesized aerosol component and typically will be less than the radiometric calibration uncertainties of Earth-orbiting sensors. When the aerosol is strongly absorbing, the method can fail; however, the potential for failure is easy to anticipate a priori. An obvious application of our technique is to provide a basis for the estimation of aerosol properties with Earth-orbiting sensors, e.g., the Multiangle Imaging Spectroradiometer.     

Accurate modeling of spectral fine-structure in Earth radiance spectra measured with the Global Ozone Monitoring Experiment

We present what we believe to be a novel approach to simulating the spectral fine structure (<1 nm) in measurements of spectrometers such as the Global Ozone Monitoring Experiment (GOME). GOME measures the Earth's radiance spectra and daily solar irradiance spectra from which a reflectivity spectrum is commonly extracted. The high-frequency structures contained in such a spectrum are, apart from atmospheric absorption, caused by Raman scattering and by a shift between the solar irradiance and the Earth's radiance spectrum. Normally, an a priori high-resolution solar spectrum is used to simulate these structures. We present an alternative method in which all the required information on the solar spectrum is retrieved from the GOME measurements. We investigate two approaches for the spectral range of 390-400 nm. First, a solar spectrum is reconstructed on a fine spectral grid from the GOME solar measurement. This approach leads to undersampling errors of up to 0.5% in the modeling of the Earth's radiance spectra. Second, a combination of the solar measurement and one of the Earth's radiance measurement is used to retrieve a solar spectrum. This approach effectively removes the undersampling error and results in residuals close to the GOME measurement noise of 0.1%.     

Surface temperature correction for active infrared reflectance measurements of natural materials

Land surface temperature algorithms for the moderate resolution imaging spectroradiometer satellite instrument will require the spectral bidirectional reflectance distribution function (BRDF) of natural surfaces in the thermal infrared. We designed the spectral infrared bidirectional reflectance and emissivity instrument to provide such measurements by the use of a Fourier transform infrared spectrometer. A problem we encountered is the unavoidable surface heating caused by the source irradiance. For our system, the effects of the heating can cause a 30% error in the measured BRDF The error caused by heating is corrected by temporally curve fitting the radiance signal. This curve-fitting technique isolates the radiance caused by reflected irradiance. With this correction, other factors dominate the BRDF error. It is now ~5% and can be improved further. The method is illustrated with measurements of soil BRDF.     

Reflectance-based calibration of SeaWiFS. II. Conversion to radiance

For instruments that carry onboard solar diffusers to orbit, such as the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS), it is possible to convert the instrument's reflectance measurements to radiance measurements by knowledge of the solar irradiance. This process, which generally requires the application of a solar irradiance model, is described. The application of the irradiance model is separate from the measurements by the instrument and from the instrument's reflectance calibration. In addition, SeaWiFS was calibrated twice before launch for radiance response by use of radiance sources with calibrations traceable to the National Institute of Standards and Technology. With the inclusion of the at-launch diffuser-based radiance calibration, SeaWiFS has three possible radiance calibrations forthe start of on-orbit operations. The combination of these three into a single calibration requires changes of 4% or less for the current at-launch radiance calibration of the instrument. Finally, this process requires changes of 4% or less for the reflectance calibration coefficients to provide consistency among the radiance calibration, the reflectance calibration, and the solar irradiance.     

Sampling period criterion in a scanning-beam technique

The scanning-beam technique for measuring the response of a detector to an irradiance is analyzed. With this method the irradiance responsivity is determined by integration of the spatial responsivity. Since in practice the integration is approximated by a summation over steps with a finite step size, errors are introduced. It is shown both theoretically and experimentally that the error vanishes when the reciprocal step size lies beyond the diffraction limit. Furthermore, comparison shows that experiment and theory are in good agreement.     

Field observations of the relation between satellite and sea radiances in coastal waters

Estimates of the different contributions to the satellite radiance above the outer Oslofjord are presented. The contribution from the sea is of the order of 10% of the total signal, and the part due to reflection from the sea surface constitutes 10-20%. The presence of land may increase the satellite radiance up to 4-9%, but such effects, which are probably reduced to 1/e at a distance of 1 km from the coast, cannot be detected in the present measurements. In situ observations of the marine radiance are corrected for shadings by ship and instrument and for varying solar altitude. The average correction for the self-shading effect of the marine instrument becomes 30-50% in these waters. The linear relations between satellite and sea radiances are determined with correlation coefficients of better than 0.95. The observed minimum value of the satellite radiance (or darkest pixel) is not a satisfactory approximation for the atmospheric correction. It is concluded that, in coastal waters and at the present stage, satellite observations have to be combined with field measurements to obtain reliable results.     

Theory of equidistant three-dimensional radiance measurements with optical microprobes

Fiber-optic radiance microprobes, increasingly applied for measurements of internal light fields in living tissues, provide three-dimensional radiance distribution solids and radiant energy fluence rates at different depths of turbid samples. These data are, however, distorted because of an inherent feature of optical fibers: nonuniform angular sensitivity. Because of this property a radiance microprobe during a single measurement partly underestimates light from the envisaged direction and partly senses light from other directions. A theory of three-dimensional equidistant radiance measurements has been developed that provides correction for this instrumental error using the independently obtained function of the angular sensitivity of the microprobe. For the first time, as far as we know, the measurements performed with different radiance microprobes are comparable. An example of application is presented. The limitations of this theory and the prospects for this approach are discussed.     

Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic

The knowledge on the optics of fogbows is scarce, and their polarization characteristics have never been measured to our knowledge. To fill this gap we measured the polarization features of 16 fogbows during the Beringia 2005 Arctic polar research expedition by imaging polarimetry in the red, green and blue spectral ranges. We present here the first polarization patterns of the fogbow. In the patterns of the degree of linear polarization p, fogbows and their supernumerary bows are best visible in the red spectral range due to the least dilution of fogbow light by light scattered in air. In the patterns of the angle of polarization α fogbows are practically not discernible because their α-pattern is the same as that of the sky: the direction of polarization is perpendicular to the plane of scattering and is parallel to the arc of the bow, independently of the wavelength. Fogbows and their supernumeraries were best seen in the patterns of the polarized radiance. In these patterns the angular distance δ between the peaks of the primary and the first supernumerary and the angular width σ of the primary bow were determined along different radii from the center of the bow. δ ranged between 6.08° and 13.41°, while σ changed from 5.25° to 19.47°. Certain fogbows were relatively homogeneous, meaning small variations of δ and σ along their bows. Other fogbows were heterogeneous, possessing quite variable δ- and σ-values along their bows. This variability could be a consequence of the characteristics of the high Arctic with open waters within the ice shield resulting in the spatiotemporal change of the droplet size within the fog.     

Systematic Errors in Laser Gain, Saturation Irradiance, and Cavity Loss Measurements and Comparison with a HCN Laser.

A pair of laser parameters of considerable practical interest are the small signal gain and saturation irradiance of the gain medium. These are commonly measured by observing the dependence of the output power on some adjustable cavity loss parameter and comparing the measured data with the predictions of a suitable laser model. Because of the inevitable approximations in this model the resulting estimates of gain and saturation irradiance are always affected to some extent by systematic errors. The small-gain, plane-wave, mean-field, and pure homogeneous or inhomogeneous line-broadening approximations are considered, with estimates of the magnitudes of these errors being presented for the case in which the gain, the saturation irradiance, and the cavity loss are fitted to the data. It is shown that these errors can be quite substantial, and therefore accurate absolute measurements of the three laser parameters can be quite difficult to obtain using the variable loss method. As an illustration of these errors, a comparison between the measured output power from a HCN laser and the power predicted using experimentally measured gain and saturation irradiance values is shown. The poor quality of these predictions illustrates the serious effects that the systematic errors can have, although an alternative analysis in which the cavity loss is supplied and only the gain and saturation irradiance fitted is also shown and gives good predictions despite inaccuracies in the model.     

Toward closure of upwelling radiance in coastal waters

We present three methods for deriving water-leaving radiance L(w)(lambda) and remote-sensing reflectance using a hyperspectral tethered spectral radiometer buoy (HyperTSRB), profiled spectroradiometers, and Hydrolight simulations. Average agreement for 53 comparisons between HyperTSRB and spectroradiometric determinations of L(w)(lambda) was 26%, 13%, and 17% at blue, green, and red wavelengths, respectively. Comparisons of HyperTSRB (and spectroradiometric) L(w)(lambda) with Hydrolight simulations yielded percent differences of 17% (18%), 17% (18%), and 13% (20%) for blue, green, and red wavelengths, respectively. The differences can be accounted for by uncertainties in model assumptions and model input data (chlorophyll fluorescence quantum efficiency and the spectral chlorophyll-specific absorption coefficient for the red wavelengths, and scattering corrections for input ac-9 absorption data and volume scattering function measurements for blue wavelengths) as well as radiance measurement inaccuracies [largely differences in the depth of the L(u)(lambda, z) sensor on the HyperTSRB].     

Portable Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity

A hand-held, battery-powered Fourier transform infrared spectroradiometer weighing 12.5 kg has been developed for the field measurement of spectral radiance from the Earth's surface and atmosphere in the 3-5-μm and 8-14-μm atmospheric windows, with a 6-cm(-1) spectral resolution. Other versions of this instrument measure spectral radiance between 0.4 and 20 μm, using different optical materials and detectors, with maximum spectral resolutions of 1 cm(-1). The instrument tested here has a measured noise-equivalent delta T of 0.01 °C, and it measures surface emissivities, in the field, with an accuracy of 0.02 or better in the 8-14-μm window (depending on atmospheric conditions), and within 0.04 in accessible regions of the 3-5-μm window. The unique, patented design of the interferometer has permitted operation in weather ranging from 0 to 45 °C and 0 to 100% relative humidity, and in vibration-intensive environments such as moving helicopters. The instrument has made field measurements of radiance and emissivity for 3 yr without loss of optical alignment. We describe the design of the instrument and discuss methods used to calibrate spectral radiance and calculate spectral emissivity from radiance measurements. Examples of emissivity spectra are shown for both the 3-5-μm and 8-14-μm atmospheric windows.     

Estimation of ozone with total ozone portable spectroradiometer instruments. I. Theoretical model and error analysis

Inexpensive devices to measure solar UV irradiance are available to monitor atmospheric ozone, for example, total ozone portable spectroradiometers (TOPS instruments). A procedure to convert these measurements into ozone estimates is examined. For well-characterized filters with 7-nm FWHM bandpasses, the method provides ozone values (from 304- and 310-nm channels) with less than 0.4% error attributable to inversion of the theoretical model. Analysis of sensitivity to model assumptions and parameters yields estimates of ±3% bias in total ozone results with dependence on total ozone and path length. Unmodeled effects of atmospheric constituents and instrument components can result in additional ±2% errors.     

Algorithms for ocean-bottom albedo determination from in-water natural-light measurements

A method for determining the ocean-bottom optical albedo R(b) from in-water upward and downward irradiance measurements at a shallow site is presented, tested, and compared with a more familiar approach that requires additional measurements at a nearby deep-water site. Also presented are two new algorithms for estimating R(b) from measurements of the downward irradiance and vertically upward radiance. All methods performed well in numerical situations at depths at which the influence of the bottom on the light field was significant.     

Radiometer for ensuring traceability of measurements by sensitive infrared detectors

An analysis is made of the errors and results of metrological certification of standard (reference) irradiance and radiance radiometers. Translated from Izmeritel'naya Tekhnika, No. 12, pp. 31–34, December, 1997.     

Remote-sensing reflectance determinations in the coastal ocean environment: impact of instrumental characteristics and environmental variability

Three independent ocean color sampling methodologies are compared to assess the potential impact of instrumental characteristics and environmental variability on shipboard remote-sensing reflectance observations from the Santa Barbara Channel, California. Results indicate that under typical field conditions, simultaneous determinations of incident irradiance can vary by 9-18%, upwelling radiance just above the sea surface by 8-18%, and remote-sensing reflectance by 12-24%. Variations in radiometric determinations can be attributed to a variety of environmental factors such as Sun angle, cloud cover, wind speed, and viewing geometry; however, wind speed is isolated as the major source of uncertainty. The above-water approach to estimating water-leaving radiance and remote-sensing reflectance is highly influenced by environmental factors. A model of the role of wind on the reflected sky radiance measured by an above-water sensor illustrates that, for clear-sky conditions and wind speeds greater than 5 m/s, determinations of water-leaving radiance at 490 nm are undercorrected by as much as 60%. A data merging procedure is presented to provide sky radiance correction parameters for above-water remote-sensing reflectance estimates. The merging results are consistent with statistical and model findings and highlight the importance of multiple field measurements in developing quality coastal oceanographic data sets for satellite ocean color algorithm development and validation.