Wave-Induced Fluctuations in Underwater Light Field: Analysis of Data from RaDyO Experiments

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1 DISTRIBUTION STATEMENT A. Approve for public release; istribution is unlimite. Wave-Inuce Fluctuations in Unerwater Light Fiel: Analysis of Data from RaDyO Experiments Dariusz Stramski Marine Physical Laboratory Scripps Institution of Oceanography University of California at San Diego La Jolla, CA phone: (5) fax: (5) Awar Number: N LONG-TERM GOALS This project is part of the Raiance in a Dynamic Ocean (RaDyO) program which aims at eveloping an unerstaning of variability in unerwater light fiel an its relation to ynamic processes within the ocean-atmosphere bounary layer. OBJECTIVES We investigate fluctuations in unerwater light fiel prouce by sea surface waves uner various bounary conitions. Our objectives focus on the characterization of wave-inuce fluctuations in ownwelling irraiance an raiance as a function of various environmental parameters an epth of observation. The central theme of our stuy is to characterize the most intense light fluctuations at shallow epths prouce by surface wave focusing uner sunny conitions. The focusing events occur in the form of high-amplitue short-uration pulses, which we refer to as light flashes. The specific objectives of this project over the past year were to analyze fiel ata collecte uring the RaDyO experiments carrie out in an 9 with special emphasis on the characterization of methoology for investigating wave-inuce light fluctuations an probability istributions of instantaneous irraiance within the near-surface ocean uner sunny conitions. APPROACH As reporte previously, we evelope a special instrument, an Unerwater Porcupine Raiometer System, which provies a capability to measure wave-inuce fluctuations in ownwar irraiance an raiance with a high sampling frequency of 1 khz. Our approach to fiel measurements involve the acquisition of time-series ata of light fluctuations with the Porcupine system at various epths within the near-surface ocean, typically at epths from about.5 or 1 m to m uner sunny conitions. Typical -min time-series obtaine with the Porcupine system using the sampling frequency of 1 khz inclues, ata points for each of 3 light sensors of the system. Our approach in this project involves the use of various statistical methos for the analysis of these time-series ata. These methos 1

2 provie several statistical characteristics of light fluctuations such as statistical moments, probability ensity function, an spectral ensity function. Special methos of ata analysis, referre to as a threshol-crossing analysis, are also use to provie the statistics escribing the frequency an uration of wave-focusing events referre to as light flashes. WORK COMPLETED We complete processing an quality control of all ata of light fluctuations collecte with the Porcupine instrument uring three fiel experiments, the RaDyO experiments conucte from R/P FLIP in the Santa Barbara Channel an off Hawaii Islans, as well as our aitional experiment conucte from the Aqua Alta Research Platform in the Ariatic Sea. We complete analyses of ata with focus on methoological issues associate with measurements an analysis of unerwater light fluctuations an characterization of probability istributions of ownwar irraiance within the near-surface ocean uner sunny conitions. These analyses resulte in the completion of two papers uring the reporting perio. Both papers have been accepte for publication in Journal of Geophysical Research (Darecki et al., in press; Gernez et al., in press). We continue the analysis of our ata, which is currently focuse on the characterization of power spectra of irraiance fluctuations an statistical properties of light flashes cause by wave focusing. RESULTS Our results show that the unerwater light fiel within the near-surface ocean shows large fluctuations cause by focusing of sunlight by surface waves uner sunny conitions. The ownwelling light at near-surface epths can fluctuate greatly on times scales as short as millisecons an spatial scales less than 1 cm. In the paper by Darecki et al. (in press) we emonstrate that specially esigne raiometers, ata acquisition systems, an sampling strategies are require to fully resolve the unerwater effects of wave focusing an to ensure the aequacy of the collecte ata for the characterization of light fluctuations within the near-surface ocean uner sunny conitions. Most importantly, these requirements pertain to resolving the shortest temporal scales (~1 - ms) an the smallest spatial scales (~1-5 mm) of light fluctuations associate with wave focusing at near-surface epths. Typical commercial unerwater raiometers that have been in common use in optical oceanography o not meet these requirements. Much of the past experimental work evote to unerwater light fluctuations i not satisfy these requirements either, an thus o not necessarily provie reliable ata on fluctuations within the top few meters of the ocean uner sunny conitions. During the early phase of the RaDyO program we evelope an Unerwater Porcupine Raiometer System (Figure 1). The paper by Darecki et al. (in press) escribes the Porcupine instrument an key aspects of the acquisition an processing of ata obtaine with this instrument. The istinctive features of the Porcupine instrument inclue multiple sensors for measuring the ownwar irraiance an raiance, a capability to properly resolve short temporal an small spatial scales of wave focusing at near-surface epths, an a capacity for acquiring high volumes of time-series ata of light fluctuations. Representative example results of wave-inuce light fluctuations obtaine with the Porcupine instrument uring fiel experiments as part of the RaDyO program are also presente. These results are use to support specific requirements of harware esign, ata acquisition protocols, an

3 computational methos involve in ata analysis. In particular, our results show that the irraiance collector of a few millimeters in iameter or smaller is require to provie aequate measurement of light flashes prouce by wave focusing. The measurements with larger irraiance collectors can result in eceptive reuction of the measure intensity of fluctuations (Figure ). The brightest flashes of irraiance or raiance can excee the time-average irraiance or raiance by an orer of magnitue an the uration of flashes is typically on the orer of millisecons to tens of millisecons. The intensity of light fluctuations ecreases rapily with epth an is higher at longer light wavelengths compare with shorter wavelengths within the visible spectral range (Figure 3). The increase in win spee beyon about 5 m s -1, an hence an increase in the surface roughness, also result in the reuce intensity of light fluctuations. Whereas the main focus of the paper by Darecki et al. (in press) is on the methoology of measurements an ata analysis of wave-inuce light fluctuations at near-surface epths uner sunny conitions, the other paper by Gernez et al. [this issue] is focuse on specific aspects of statistical analysis of ata obtaine with the Porcupine instrument uner such conitions. This paper escribes the first systematic stuy eicate to the characterization of the probability istribution of instantaneous values of ownwar irraiance E (t) within the near-surface ocean when the sun is not covere by clous. Our analysis of time-series ata of wave-inuce fluctuations in unerwater ownwar irraiance within the green spectral ban [E (t) at λ = 53 nm] collecte at ifferent epths uner sunny conitions emonstrates large vertical changes in the probability istribution of instantaneous irraiance within the examine near-surface oceanic layer, i.e., from about 1 to m (Figure ). In the first few meters near the surface, the probability istribution of irraiance is highly skewe to the right an heavy-taile. This is because of the occurrence of intense wave focusing events that excee the mean irraiance, E, several-fol or by tens of stanar eviations. We teste several probability moels, incluing log-normal, Gumbel, Fréchet, log-logistic, an Pareto, which were originally evelope to escribe skewe an heavy-taile istributions. None of the moels shows consistently goo performance in terms of fitting the experimental istribution of irraiance over a broa range of values, especially within the right tail of the experimental istribution where the probability of relatively high irraiance values is less than %. This portion of the istribution correspons approximately to light flashes with E > 1.5 E, where E is the time-average ownwar irraiance. We foun, however, that the remaining part of the probability istribution covering all irraiance values smaller than the 9th percentile can be escribe with a reasonable accuracy (i.e., within %) with a log-normal moel for all measurements from the top m of the ocean inclue in our analysis. This range of the istribution is approximately equivalent to irraiance values E < 1.5 E. The vertical changes in the probability istribution of irraiance are characterize by rapi ecrease in the values of skewness an excess kurtosis with epth (Figure 5). Close to the surface at epths less than 1 m, these coefficients can assume values larger than 3 an, respectively. As the intensity of irraiance fluctuations ecreases with epth, the probability istribution tens towar a function symmetrical aroun the mean like the normal probability istribution. At the m epth, both the skewness an excess kurtosis are reuce to nearly zero, which is consistent with the normal istribution. This result suggests that the irraiance istribution approaches the Gaussian istribution with increasing epth. Such vertical changes can be attribute to an increasing role of iffuse light an a ecreasing role of irect sunlight, which ampen irraiance fluctuations with epth. 3

4 IMPACT/APPLICATIONS The major impact of this project is to provie an unerstaning of wave-inuce fluctuations in unerwater light fiel. This phenomenon has been scantily investigate in the past. Our measurements an analyses provie critical information for achieving broaer science goals of the RaDyO program, incluing the evelopment of couple surface wave-raiative transfer moels. Our finings are also expecte to have broaer implications beyon the isciplines of ocean optics an physics, specifically in the areas of ocean biology an photochemistry. RELATED PROJECTS This effort is relate to our previous project fune uner the RaDyO program an other projects supporte by that program. REFERENCES Darecki, M., D. Stramski, an M. Sokolski, Measurements of high-frequency light fluctuations inuce by sea surface waves with an Unerwater Porcupine Raiometer System, J. Geophys. Res., oi:.9/11jc733, in press. Gernez, P., D. Stramski, an M. Darecki, Vertical changes in the probability istribution of ownwar irraiance within the near-surface ocean uner sunny conitions, J. Geophys. Res., oi:.9/11jc715, in press. PUBLICATIONS Darecki, M., D. Stramski, an M. Sokolski, Measurements of high-frequency light fluctuations inuce by sea surface waves with an Unerwater Porcupine Raiometer System, J. Geophys. Res., oi:.9/11jc733, in press. Gernez, P., D. Stramski, an M. Darecki, Vertical changes in the probability istribution of ownwar irraiance within the near-surface ocean uner sunny conitions, J. Geophys. Res., oi:.9/11jc715, in press.

5 Irraiance sensors Raiance sensors Vane Control unit Rotator Cable Figure 1. An Unerwater Porcupine Raiometer System with its major components inicate. The presente configuration of the instrument consists of six irraiance sensors, each with ifferent size of plane cosine collector (from.5 mm to 3 mm), an seventeen raiance sensors for observations at ifferent zenith angles within two orthogonal azimuthal planes. Note that the configuration of the sensors use routinely uring the RaDyO experiments in the Santa Barbara Channel an off Hawaii Islans was ifferent than that shown in this figure. For example, seven irraiance sensors, each equippe with the same size of collector (.5 mm) but ifferent spectral filters, were use uring the RaDyO experiments. 5

6 D =.5 mm, z =.5 m X(t) = E (t) / E X(t) = E (t) / E X(t) = E (t) / E X(t) = E (t) / E D =.5 mm, z =.7 m D = 3 mm, z =.7 m D = 3 mm, z =.5 m Time t [ s ] Figure. Example fluctuations in ownwelling irraiance measure at two epths, z =.5 m an.7 m, with the Porcupine irraiance sensors equippe with the interference filter centere at 53 nm an cosine collectors having a iameter D of.5 mm an 3 mm as inicate. The time-series ata are shown for the normalize irraiance, X(t) = E(t)/ E. The measurements were mae in the Ariatic Sea on June 1, 9 at 9: am an 9:5 am local time uner clear skies, win spee U =.7 m s-1, solar zenith angle θs = 35o - 37o, an the beam attenuation coefficient of seawater at 555 nm, c(555) =.33 m-1.

7 (a) Depth z [ m ] 3 nm 53 nm 7 nm Coefficient of variation σ E / E Coefficient of variation σ E / E (b) 3.9 ms -1.3 ms ms -1 W =.3 ms ms Light wavelength λ [ nm ] Figure 3. (a) The epth epenence of the coefficient of variation of the ownwelling irraiance at three light wavelengths (3, 53, an 7 nm) base on measurements mae in the Santa Barbara Channel on September 11, between 11:35 am an 1:5 pm local time uner sunny conitions, solar zenith angle θ s = 3 o - 33 o, win spee W =.1 -. m s -1, an the beam attenuation coefficient of seawater at 555 nm, c(555) =. m -1. (b) Spectral epenence of the coefficient of variation of ownwelling irraiance measure at near-surface epths uner sunny conitions an ifferent win-wave conitions as inicate by the win spee W. The measurements were mae in the Santa Barbara Channel on the following 5 ays in : September 15 (:15 pm local time, W =.3 m s -1 ), Sept. 1 (1:55 pm, W =.3 m s -1 ), Sept. 1 (9: am, W = 5. m s -1 ), Sept. 19 (1:1 pm, W = 7. m s -1 ), an Sept. (9: am, W = 3.9 m s -1 ) uner sunny conitions, epth z = m, solar zenith angle θ s = o - o, an the beam attenuation coefficient of seawater at 555 nm, c(555) = m -1. 7

8 Figure. (a) Probability ensity function, f(y), of the stanarize ownwelling irraiance, Y [E (t)/ E - µ] / σ, base on example measurements performe in the Santa Barbara Channel on September 11, 9 within a perio of 1.5 hours, uring which the solar zenith angle θ s varie from about 3.3 o to 33.1 o an the win spee U from. m s -1 to. m s -1. The parameters µ an σ represent the mean an stanar eviation of the normalize ownwelling irraiance, X E (t)/ E. The experimental probability ensity functions are shown as colore lines for four ifferent epths as inicate. For comparison, the theoretical probability ensity function of a normal istribution is shown as grey line. (b) Complementary cumulative istribution functions, P(X > x t ), of the normalize ownwelling irraiance, X E (t)/ E, are shown as soli lines for the same example measurements as in panel (a). For comparison, the ashe lines show the complementary cumulative istribution functions, P(X > x t ), corresponing to the theoretical normal istribution. The values of x t represent specific threshol values of X, for which the probability of the complementary cumulative istribution function is etermine.

9 Figure 5. (a) The skewness coefficient, γ 1, of the normalize ownwelling irraiance, X E (t)/ E, as a function of epth for 1 measurements mae in the Ariatic Sea (grey squares), 3 measurements from the Santa Barbara Channel (open circles), an 9 measurements from the Hawaii experiment (black triangles). The solar zenith angle for this entire ata set consisting of measurements varies between 1. o an 39.9 o, an the win spee between 1.3 m s -1 an 11.1 m s -1. The ashe vertical line at γ 1 = inicates the skewness corresponing to a symmetrical istribution, such as a normal istribution. (b) Same as panel (a) but for the coefficient of excess kurtosis γ. (c) Same as panel (a) but the coefficient of skewness was calculate for the logtransforme normalize ownwelling irraiance, lnx ln[e (t)/ E ] rather than the normalize irraiance X. () Same as panel (b) but the coefficient of excess kurtosis was calculate for the logtransforme normalize ownwelling irraiance, lnx ln[e (t)/ E ]. 9