modeling the diurnal variability of sea surface temperatures · s. pimentel,1 k. haines,2 and n. k....

Modeling the diurnal variability of sea surface temperatures

S. Pimentel,1 K. Haines,2 and N. K. Nichols3

Received 23 October 2007; revised 5 August 2008; accepted 20 August 2008; published 5 November 2008.

[1] In this study a one-dimensional mixed layer ocean model is customized for thepurpose of estimating the diurnal signal of temperature in the near-surface ocean layer,generically referred to as sea surface temperature (SST). The model is initially runwith data from three mooring locations. It is then demonstrated how operationalforecast data sets can be utilized to estimate diurnal signals over a wide area. Dailydiurnal variability maps are produced for a weeklong period over the Atlantic Ocean.These maps highlight the transient nature of diurnal SST signals with day to daychanges in their magnitude and spatial distribution. The resulting diurnal variabilitymaps are evaluated using a combination of infrared and microwave satellite-derivedSST observations taken over the day. These matchups result in a mean error of 0.09�Cand a standard deviation of 0.54�C. Advantages of modeling the diurnal cycle asopposed to using a persistence assumption are discussed.

Citation: Pimentel, S., K. Haines, and N. K. Nichols (2008), Modeling the diurnal variability of sea surface temperatures, J. Geophys.

Res., 113, C11004, doi:10.1029/2007JC004607.

1. Introduction

[2] Intense diurnal warming of the surface of the oceancommonly occurs in low wind and clear sky conditions,when the wind-driven turbulence is insufficient to erode thenear-surface restratification caused by absorption of solarradiation during the day. This buoyant highly stratifiedwarm layer leads to an afternoon diurnal temperature peak,after which the amplitude decays as surface cooling triggersoceanic convection and surface wind stress causes verticalshear instability, breaking down the diurnal thermocline[Price et al., 1986]. Diurnal warming was reported byStommel [1969] and has since been investigated by anumber of authors at various locations [e.g., Cornillonand Stramma, 1985; Price et al., 1986; Webster et al.,1996; Stuart-Menteth et al., 2003].[3] Depending on how it is measured, the near-surface

warming in favorable conditions can be 3.5�C [Stramma etal., 1986], although a diurnal variability of over 6�C hasbeen recorded [Flament et al., 1994]. In contrast, when anactive wind-driven mixed layer is present, the diurnalamplitude of surface temperature seldom exceeds a fewtenths of a degree.[4] Satellites now provide global synoptic measurements

of sea surface temperatures (SST) which can be valuable formany purposes, but up until now these measurements havebeen difficult to make with high absolute accuracy. Onereason is because SST retrievals by satellite (both infrared

and microwave) are sensitive to a conductive diffusion-dominated sublayer of the ocean surface where the effectiveskin temperature as well as the near-surface layer down to acouple of meters is strongly influenced by a diurnal warm-ing effect. Sometimes the local time of SST observations arenot taken into account at all when merging satellite data toproduce observational products [e.g., Reynolds and Smith,1994]. Another common approach is to flag and removeobservations that are taken during the day in low windspeed conditions; this then reduces the likelihood of a biasdue to diurnal warming. This is the approach taken by theUK Meteorological Office (UKMO) in producing its Oper-ational Sea Surface Temperature and Ice Analysis (OSTIA)[Stark and Donlon, 2006; Stark et al., 2007], where daytimeobservations recorded in wind speeds below 6 m s�1 areexcluded. However, this is far from an ideal situation aswinds speeds of less than 6 ms�1 account for over 40% ofthe total occurrence of hourly averaged wind speeds overthe ocean [see Martin, 2004, Figure 2.1]. Moreover weakwinds are concentrated in the tropics and subtropics wherethe majority of ocean to atmosphere heat flux occurs andshifts in their patterns affect the global heat flux balance[Shankaranarayanan and Donelan, 2001]. Therefore, accu-rate quantification of diurnal signals are required in order tomake the best use of satellite-derived SST observations.[5] Stuart-Menteth et al. [2003] produced monthly aver-

aged and interannual diurnal warming maps derived solelyfromAdvanced Very High Resolution Radiometer (AVHRR)day/night matchup observations. Their study revealed theextent of diurnal warming at midlatitudes and the tropics andsuggested the need for the diurnal cycle to be included innumerical models.[6] The diurnal cycle is a fundamental signal in the

climate system [Yang and Slingo, 2001], and is increasinglyseen to have an impact on longer-timescale variations.Bernie et al. [2005] and Shinoda and Hendon [1998] show

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1Department of Earth Sciences, Simon Fraser University, Burnaby,British Columbia, Canada.

2Environmental Systems Science Centre, University of Reading,Reading, UK.

3Department of Mathematics and Department of Meteorology,University of Reading, Reading, UK.

Copyright 2008 by the American Geophysical Union.0148-0227/08/2007JC004607$09.00

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how the rectification of the diurnal cycle of SST onto thedaily mean SST affects the magnitude of the variability ofintraseasonal SST in coupled atmosphere-ocean simula-tions. The diurnal variability of SST has a major impacton the time integrated air-sea heat flux calculations asexplained by Price et al. [1986], Webster et al. [1996],and Danabasoglu et al. [2006]. Improved accuracy isattained in air-sea heat flux calculations if skin ratherthan foundation SST is used and temporal averaging ofSST values are avoided or limited. Fairall et al. [1996a]found that, averaged over the 70 days sampled duringCoupled Ocean-Atmosphere Response Experiment(COARE), the cool skin increases the average atmo-spheric heat input to the ocean by about 11 W m�2;the diurnal warm layer decreases it by about 4 W m�2

(but the effect can be 50 W m�2 at midday). Diurnalvariability also has an important influence on mixed layerdynamics by enhancing the strength of mixing across thethermocline [McCreary et al., 2001; Shinoda, 2005]. Inaddition Katsaros and Soloviev [2004] and Katsaros et al.[2005] have shown how horizontal SST discontinuities arediminished by diurnal variability. Thus an ability to accu-rately and effectively simulate and measure the diurnalvariability of SSTs will be of great benefit.[7] A strong boost to support the continuation and

improvement of satellite SST measurements would comefrom their use in operational ocean forecast and NWPmodels. However, the current generation of these modelsdo not resolve the diurnal SST cycle and therefore prob-lems are encountered when assimilating SST observationswhich are diurnally ‘corrupted’, which can result in alias-ing. To address some of these issues, particularly the use inoperational oceanography, this study focuses on the abilityof a numerical model to provide local diurnal warmingestimates on the basis of operational ocean and NWPforecast input data.[8] The study will also use the classification of SSTs that

takes into account the vertical temperature structure of theupper ocean as introduced by Donlon et al. [2002] and usedby the Global Ocean Data Assimilation Experiment(GODAE) High-Resolution Sea Surface Temperature PilotProject (GHRSST-PP) [Donlon et al., 2007].[9] The paper proceeds as follows: A background to

diurnal cycle modeling and the model setup used in thiswork is given in section 2. Results from some initialexperiments performed at upper ocean mooring sites arepresented in section 3. This work is then extended to the useof operational data sets in section 4. In section 5 diurnalvariability maps in the Atlantic are produced and comparedto satellite-derived SST measurements. Finally conclusionsare given in section 6.

2. Modeling

2.1. Background

[10] One-dimensional modeling of the oceanic mixedlayer has been widely used in the development of turbu-lence and air-sea flux parameterizations. Such models arealso suitable for modeling diurnal variability of SST as theycan have a much greater near-surface vertical resolutionthan can be achieved in a full ocean GCM. Mixed layermodeling can generally be categorized into two broad

approaches: bulk and diffusion. Bulk models attempt tomodel the mixed layer in an integral sense [e.g., Kraus andTurner, 1967; Price et al., 1986]. The governing equationsof heat and momentum are integrated over the mixed layerand the balance of heat and momentum over the entiremixed layer are adjusted by the effects of momentum andbuoyancy fluxes. On the other hand diffusion modelsdirectly parameterize the turbulent mixing and diffusion inthe mixed layer [e.g., Mellor and Yamada, 1982; Large etal., 1994; Kantha and Clayson, 1994].[11] The first detailed modeling study of the diurnal cycle

was by Price et al. [1986] who developed a bulk modeldependent on the generation of shear instability at the baseof the mixed layer. This model was also used by Shinodaand Hendon [1998] and Shinoda [2005] to model diurnalvariability in the western equatorial Pacific. The bulk modelby Kraus and Turner [1967] was compared to the diffusionmodel of Kantha and Clayson [1994] in a study byHorrocks et al. [2003]. They found the Kraus-Turner modelcould predict when diurnal thermoclines would form, butcould not accurately determine their magnitude. The mainlimitation was the reliance on mechanical and buoyancydriven mixing, which under strong solar heating and lowwind speeds becomes very low leading to surface heat buildup, with no mechanism such as diffusion or conduction todraw heat downward. The diffusion approach of Kantha andClayson [1994] was more effective at producing downwardmixing and thus predicting diurnal amplitudes. Hallsworth[2006] compared the Price bulk model with a diffusion typemodel called the General Ocean Turbulence Model (GOTM)(see section 2.2) at two mooring sites and also consistentlyfoundGOTMperforming better at modeling the diurnal cycleof near-surface temperatures.[12] Model experiments in the western Pacific warm pool

suggest an upper layer resolution of order 1 m is required tocapture 90% of the diurnal variability [Bernie et al., 2005]from the TAO data. However satellite observations resolve amuch thinner layer and Horrocks et al. [2003] used a gridlayer of 2 cm, increasing exponentially with depth to 60 cm,when comparing model output to Advanced Along-TrackScanning Radiometer (AATSR) observations.[13] The penetration of solar radiation is also critical for

diurnal modeling. A single spectral band parameterization[Paulson and Simpson, 1977] is still widely used [e.g.,Bernieet al., 2005; Shinoda, 2005] despite its crude structure.Horrocks et al. [2003] implemented a 9-band parameteriza-tion [Paulson and Simpson, 1981] while Hallsworth [2006]experimented with several parameterizations includingdecomposing the full solar spectrum into 278 intervals. Inrecent years more attention has been given to the biologicalimpact on solar absorption [Ohlmann et al., 2000].[14] To attain the temporal resolution for diurnal modeling

studies data from the TOGA COARE sites are often used,where high-frequency meteorology (every 15 min) is avail-able [Webster et al., 1996; Shinoda, 2005; Bernie et al.,2005]. Bernie et al. [2005] performed experiments usingdifferent flux frequencies and concluded that to capture 90%of the diurnal variability of SST, 3 hourly flux forcing wasrequired. However, Horrocks et al. [2003] used 6 hourlysurface fluxes from UKMO NWP analyses and then gener-ated only the solar flux at higher frequency.

C11004 PIMENTEL ET AL.: MODELING THE DIURNAL VARIABILITY OF SST

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[15] These previous studies have guided the modelingchoices here.

2.2. Model Setup

[16] For this study the GOTM model was used; originallypublished in 1999 it has been regularly extended since[Umlauf et al., 2005]. For the purposes of this study weconstruct a nonuniform grid with 150 vertical levels, re-solving a depth down to 150 m. The top grid box is 0.030 mthick, while the bottom box is 3.015 m thick, on the basis ofthe formula

hi ¼ 150tanh i

50

� �� tanh i�1

50

� �tanh 3ð Þ ; ð1Þ

where hi represents the thickness of the ith model layer. Thisgrid distribution results in 67 model layers within the top10 m of ocean. A time step of 30 seconds is used.[17] We have updated the air-sea flux module in GOTM,

replacing the Kondo [1975] air-sea flux parameterizationwith the superior TOGA-COARE algorithm [Fairall et al.,1996b, 2003], and we have incorporated a cool skinparameterization [Fairall et al., 1996a] for use in calculat-ing upwelling longwave radiation as well as sensible andlatent heat flux. The ocean radiant heating parameterizationof Paulson and Simpson [1977] was replaced with a 9-bandparameterization [Paulson and Simpson, 1981] that coversthe complete spectral range.[18] Following Hallsworth [2006], who performed a

diurnal SST comparison study of the various turbulenceclosure schemes incorporated in GOTM, the so-called2-equation k-e turbulent kinetic energy parameterization isemployed for the mixing, (see Umlauf and Burchard [2003]for a detailed description of this turbulence closure schemeand the solution procedure). In using a fine near-surfacegrid the model can become very sensitive to the amount ofmixing being generated in the top grid boxes, particularlyin low wind speed conditions. Under low wind speedconditions the surface stress is very small and littleturbulent kinetic energy (TKE) is generated. Turbulenceschemes have a tendency to under produce TKE in suchcircumstances, but these values are of extreme importancewhen modeling the diurnal cycle. To prevent the extin-guishing of TKE an internal wave (IW) parameterization[Kantha and Clayson, 1994] was included to representinternal wave activity which always leaves a backgroundresidue of TKE. To enhance mixing at the surface a wavebreaking parameterization [Craig and Banner, 1994] wastested but was not found to improve results and was not

used in the results here. Under low wind stress conditionsthe type of surface boundary conditions (prescribed Dirich-let conditions or a flux boundary Neumann type condition)for TKE and dissipation is important, and Neumannconditions were chosen as they were found to give thebest results. Details of these tuning experiments can befound in the thesis by Pimentel [2007].

3. Buoy Simulation Experiments

[19] Initial experiments with the model were performed atthree different mooring sites, the results of which arepresented in this section.

3.1. Data

[20] Surface meteorological and ocean temperature obser-vations are obtained from the Woods Hole OceanographicInstitution (WHOI) upper ocean mooring data archive. Weuse time series from three deployments: COARE [Wellerand Anderson, 1996], Arabian Sea [Weller et al., 1998], andthe Subduction site [Moyer and Weller, 1997]. Details ofeach time series is given in Table 1. The meteorologicalvariables consist of the wind speed components u and v, airtemperature Ta, relative humidity qrh, and air pressure p.These measurements were made at heights between 2 and4 m. In addition measurements were taken of the downwel-ling shortwave radiation (SWR) and longwave, radiation(LWR), I# and QB

# respectively. An estimated typical in-stantaneous accuracy is 3% for I# and 10 W m�2 for QB

#

[see Weller and Anderson, 1996, Table A2]. The oceantemperature observations, qobs(z), at various depths z (with-in the top 150 m there are 29 observation depths in theArabian Sea, 34 at COARE, and 12 at the Subduction site)are linearly interpolated onto the model grid and are used toinitialize and validate the model simulations.[21] These rare observational time series with good

temporal resolution are ideal for diurnal warming studiesand the particular locations chosen in the tropics and higherlatitudes provide a sample of the meteorological conditionsfound in areas of the globe that experience diurnal vari-ability of SSTs.

3.2. Methodology

[22] The model profile is initialized with the observedtemperatures every 24 hours at local sunrise, and forcedwith sensible and latent heat fluxes calculated from thesurface meteorology (Table 1) using the air-sea flux algo-rithm [Fairall et al., 1996b, 2003] together with downwel-ling SWR and LWR observations.

Table 1. Locations, Deployment Duration, and Data Frequency at the Three Mooring Sitesa

Sites Location Duration Frequency

Arabian Sea 15�N, 61�E 17 Oct 1994 to qobs(z) every 15 min17 Oct 1995 u, v, Ta, qrh, and p every 7.5 min

I# and QB# every 15 min

COARE 1�S, 156�E 1 Nov 1992 to qobs(z) every 15 min1 Mar 1993 u, v, Ta, qrh, and p every 7.5 min


Subduction 26�N, 29�W 24 Jun 1991 to qobs(z) every 15 min16 Jun 1993 u, v, Ta, qrh, and p every 15 min


aCOARE, Coupled Ocean-Atmosphere Response Experiment.


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[23] Further experiments were performed with the surfacemeteorological observations and the downwelling SWR andLWR from the buoys averaged over 6 hourly periods, thenormal output format and frequency from NWP models.This allows us to assess the degradation of diurnal modelingskill that could be expected because of the effects oftemporal sampling from using the NWP products overmuch wider areas.[24] Diurnally varying solar SWR forcing is the essential

driver of the diurnal cycle. To meet the challenge ofinterpolating from 6 hourly mean values, when full directSWR observations are unavailable, the following methodwas used. Surface insolation under clear skies, I#, wascalculated at every time step using the approach of Rosatiand Miyakoda [1988]. The Reed formula [Reed, 1977]

I0 ¼ I# 1� Cnnþ 0:0019bð Þ 1� að Þ; ð2Þ

is then used to derive the total surface solar radiation, where nis the fractional cloud cover;Cn, the cloud cover coefficient isset to 0.62; b is the solar noon angle; and a the albedo. Thisformula is only used for higher cloud amounts 0.3 � n � 1,with I0 = I#(1 � a) otherwise [Gilman and Garrett, 1994].However, the cloud values, n are not directly observed atthese sites, so the 6 hourly mean observed SWR values areused together with the calculated 6 hourly mean clear skyvalues to derive 6 hourly values of n.

n ¼ 1� Iobs

I#þ 0:0019b

� �=cn: ð3Þ

[25] This technique allows the SWR to be calculated at amuch finer time resolution (at each model time step) on thebasis of a 6 hourly fixed cloud correction.[26] Equation 2 has been widely used in the oceano-

graphic community and is surprisingly accurate for such asimple expression [Taylor, 2001]. A comparative study ofthese methods by Dobson and Smith [1988] found that theReed formula gave the best long-term mean insolationvalues. Numerous studies have evaluated the precision ofequation (2) [e.g., Dobson and Smith, 1988; Schiano,1996; Kizu, 1998] finding small, but different, regionalbiases and generally supporting its use for long timeaverage insolation over the ocean. Calibration based onradiometric measurements can improve the accuracy forparticular regions, [e.g., Schiano, 1996] over the Mediter-ranean Sea reduces the transmission coefficient (used inthe calculation of I#) from 0.7 to 0.66 on the basis ofaerosol and water vapor changes.[27] Following the suggestion of Schiano [1996] the

transmission coefficient and the cloud cover coefficient

are adjusted on the basis of the SWR observations taken atthe mooring sites. To ensure over 90% of the SWRobservations fall between the clear sky and full cloudlimits of the Reed parameterization, the transmissioncoefficient was kept at 0.7 at the Subduction site, reducedto 0.63 at the COARE site, and increased to 0.74 at theArabian Sea. The cloud cover coefficient remained 0.62 atthe Subduction and Arabian Sea sites, but was increased to0.72 at the COARE site.[28] The ability of the model to replicate the sea temper-

ature records, given the observed forcing, can be assessed invarious ways. Comparisons are made between the observedand modeled ocean temperatures at various depths in thewater column. Particular interest is paid to the temperatureat the shallowest measurement, qz1obs, (where z1

obs is 0.45,0.17, and 1.0 m at COARE, Arabian Sea, and Subduction,respectively) and the ability to model its variability.[29] The magnitude of diurnal warming is defined as the

maximum SST (temperature at the shallowest observeddepth, qz1obs) minus the minimum SST, over a 24-hourwindow starting at the initialization time

Dqzobs1

¼ max0�24

qzobs1

� min0�24

qzobs1: ð4Þ

[30] In order to avoid the misinterpretation of a cooling orwarming trend over the window the maximum qz1obs is said tooccur when the temperature is greatest above the back-ground linear trend (estimated from initialization points ineach time window). Similarly the minimum qz1obs over the24-hour period is defined as the temperature that deviatesthe most below the estimated linear trend for the timewindow. The near-surface stratification is also calculated;this is given as the difference between the temperature at theshallowest observation point and the commonly observed10 m depth, as follows;

stratification ¼ qzobs1

� q10m: ð5Þ

The warm layer depth, WLD, is calculated as the depth atwhich the modeled/observed temperature drops to 0.1�Cbelow the maximum modeled/observed temperature, withinthe top 20 m. This is the same criterion used by Weller et al.[2002]. These additional parameters are used to assess themodel simulation against observational profiles from thebuoys.

3.3. Results

[31] Results, shown in Table 2, reveal root mean square(RMS) qz1obs SST errors below 0.2�C at all sites, whilediurnal warming errors are larger. The largest diurnalwarming errors are at the COARE site. However, the meanobserved diurnal warming over the entire time series isgreater at this location, 0.56�C, compared with 0.46�C atArabian Sea and 0.25�C at the Subduction site.[32] It should also be remembered that the SST is based

on the uppermost observation at each site (i.e., from slightlydifferent near surface depths). The errors in the WLD seemquite large considering the observed temperature profile isused to initialize each day. This could be revealing asensitivity of the measure to nonlocal changes in the watercolumn. The RMS error in the stratification varies only by

Table 2. Statistics From Comparisons Derived From Observations

and Model Simulations Initialized Daily at the Mooring Sites

Site

RMS Errors

qz1obs (�C)Diurnal

Warming (�C)Warm LayerDepth (m)

Stratification(�C)

COARE 0.19, 0.21a 0.36, 0.39a 13.54, 16.65a 0.19, 0.2a

Arabian Sea 0.15, 0.19a 0.23, 0.29a 11.31, 13.10a 0.13, 0.17a

Subduction 0.13, 0.15a 0.21, 0.21a 22.12, 25.22a 0.14, 0.16a

aResults obtained from model simulations forced with 6 hourly data.


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0.06�C across the sites, and is always below 0.2�C. Drift inthe modeled near-surface temperatures over the day arenegligible and the daily initialization limits the influence ofnonlocal processes within the water column. The TKE isconsidered to be in quasi-equilibrium, and remains un-changed during the initialization of the temperature profile.[33] Root mean square differences for hourly qz1obs at each

site can be viewed in Figure 1. The largest errors, asexpected, occur around midday local time when the SSTvariability is greatest. The continuing increase in the errorsafter sunset for the Arabian Sea data could be due to anaccumulation of errors resulting from occasional episodes ofnonlocal modulation of the water column.[34] The square of the correlation coefficient, R2, was

used to calculate the fraction of variability in the observeddata accounted for by the numerical model. The results arepresented in Table 3; the correlation for both hourly qz1obs anddaily peak qz1obs is strong especially at the Arabian Sea andSubduction sites where over 95% of the variance isexplained by the model.[35] The results of the reduced frequency (6 hours)

forcing experiments are only slightly different, as can beseen in the parentheses in Tables 2 and 3. An example of themodeled diurnal warming signals in this case is shown inFigure 2. This covers a 6 day period from the Arabian Seatime series. The diurnal cycles are of the order 1.5�C andthe observed variability is well replicated by the model.Some additional rapid variability is seen in the observationsparticularly at the peak of the cycle during days 162 and 163of the time series; this could be a result of wind fluctuationsor passing clouds that have been smoothed over in theforcing data. Overall the mean modeled diurnal warming

signals are 0.56�C, 0.52�C, and 0.35�C at the COARE,Arabian Sea, and Subduction sites, respectively. This com-pares with the corresponding mean observed diurnal warm-ing signals of 0.56�C, 0.46�C, and 0.25�C. Thus theaverages produced by the diurnal model are accurate towithin a tenth of a degree for each time series, with theCOARE site being most closely replicated. Another mea-sure is the timing of the diurnal peak. For the reducedfrequency forcing experiments it was found that the modelpredicts an earlier peak by 2, 10, and 53 min at the COARE,Arabian Sea, and Subduction sites, respectively.[36] Results suggest that the diurnal cycle can be effec-

tively modeled with 6 hourly forcing data, although it ispossible that there are locations where the occurrence ofsharp wind bursts around midday are more prevalent, thushampering the modeling performance. Nonetheless the stan-dard output from operational weather forecasting centers is6 hourly and the results in Tables 2 and 3 show that modelingthe diurnal cycle of SSTs over the global ocean should be apossibility. This topic is addressed in the next section.

4. NWP Forcing Experiments

[37] In this section the GOTM model is set up to useNWP forcing data on a larger spatial domain. The use ofNWP data in diurnal variability modeling is far from ideal,particularly with regards to the use of 6 hourly wind stressvalues, as the diurnal cycle can be extremely sensitive tofine-scale wind structure [Stuart-Menteth et al., 2005].However the last section showed that when GOTM isforced with 6 hourly mean data at the mooring sites it canreasonably capture the observed diurnal variability. Thiswas achieved by parameterizing the SWR at a finer resolu-tion than 6 hours.[38] In addition the NWP forcing experiments are com-

pared with satellite measurements of SSTwhich are taken atvarious times of day in order to test whether the diurnalmodeling can successfully capture some of the observedvariability. For these satellite comparisons the uppermostmodel layer at a depth of 3 cm is compared with the subskinSST satellite measurements.

4.1. Data

[39] We use the European Centre for Medium-rangeWeather Forecasting (ECMWF) 1� global meteorological

Figure 1. Hourly, time from initialization, root meansquare differences between model output, qz1obs, and buoyobservations at 0.45, 0.17, and 1.0 m at the COARE,Arabian Sea, and Subduction sites, respectively.

Table 3. Portion of Variability in the Observed Data Accounted

for by the Numerical Model

Site

Correlation Coefficient Squared (R2)

Hourly qz1obs Daily Peak qz1obsCOARE 0.80, 0.78a 0.73, 0.66a

Arabian Sea 0.99, 0.99a 0.99, 0.97a

Subduction 0.99, 0.99a 0.99, 0.98a

aResults obtained from model simulations forced with 6 hourly data.

Figure 2. Example of the modeled and observed diurnalwarming signal at the Arabian Sea site, (15�N, 61�E).


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analyses/forecasts of 6 hourly integrated fluxes at 18:00,00:00, 06:00, and 12:00 UTC, for surface solar radiation,10 m wind speed components, 2 m air temperatures, and2 m dew point temperatures, as well as sea level pressure.TheUKMOForecastingOceanAssimilationModel (FOAM)global 1� data provide analyses of ocean temperature andsalinity (at depths: 5, 15, 25, 35, 48, 67, 96, and 139 m) at00:00 UTC.[40] Satellite observations include a combination of

infrared (SEVIRI) and microwave (AMSR-E and TMI)SSTs from the GHRSST-PP Level-2 Preprocessed (L2P)products. The data used for this study have the GHRSSTestimated bias corrections applied (a correction for long-term mean biases in the sensor) and have proximityconfidence values labeled ‘acceptable’, ‘excellent’, and‘diurnal’. This choice selects observations uncontaminatedby cloud (for infrared) or rain (for microwave), butretains observations that potentially have a diurnal signal.Infrared retrieved SSTs are normally recognized as rep-resenting a skin SST, whereas the microwave retrievedSSTs are representative of a temperature just below thecool skin effect. However, the SEVIRI retrieval algorithmis validated and corrected against nighttime buoy SSTsand thus the SEVIRI SSTs provided by GHRSST aredesigned to be subskin temperatures [Merchant andLeBorgne, 2004].[41] The OSTIA product, developed at the UKMO is

based on GHRSST-PP L4, combining in situ, microwaveand infrared satellite-derived SST, and is used in modelinitialization. It deliberately excludes diurnal amplitudesby prohibiting daytime observations if wind speeds arebelow 6 m s�1. For more information on the data processingspecifications adopted for GHRSST products see Donlonand the Global Ocean Data Assimilation Experiment HighResolution Sea Surface Temperature–Pilot Project ScienceTeam [2004].

4.2. Experimental Description

[42] As in the previous section the solar flux is converted toa finer time resolution. ECMWF SWR is given as a 6 hourlyintegrated value, rather than a mean value. Integrating theReed formula over a 6 hour window gives

Z Tþ6

T

I0dt ¼Z Tþ6

T

I# 1� 0:62nþ 0:0019bð Þ 1� að Þdt; ð6Þ

where T are the 6 hourly forecast times. The left hand sideof equation (6) is set equal to the ECMWF value, andequation (6) can be rearranged to find an effective meancloud value over this window,

n ¼1þ 0:0019bð Þ

R Tþ6

TI# 1� að Þdt �

R Tþ6

TI0dt

0:62R Tþ6

TI# 1� að Þdt

: ð7Þ

[43] If it is night, so thatRTT+6I#(1 � a)dt = 0, then

persistence nk = nk�1 is assumed. A check is also made toenforce the physical cloud limits 0 � n � 1. The net surfaceSWR, I0, used in the model run is calculated every time step

using the Reed formula (2) with the 6 hourly derived cloudvalues.[44] The air-sea fluxes are calculated using the 6 hourly

forecast surface meteorology (air and dew point tempera-ture, air pressure, and u and v wind speeds) together withthe modeled SST from GOTM, whose top layer is 3cmdeep, although the air-sea flux algorithm uses the cool skinparameterization to better represent the actual interfacialtemperature at which the flux transfer takes place. Thisdynamic calculation allows feedback between the modeledSST and the fluxes, and preliminary experiments found thisto be better than using the prescribed fluxes from ECMWF[Pimentel, 2007].[45] The change in solar flux with depth into the ocean is

parameterized as a sum of exponentials

f zð Þ ¼Xni¼1

Ai exp �Kizð Þ: ð8Þ

[46] In the previous section this was determined using a9-band parameterization [Paulson and Simpson, 1981].Although the 9-band parameterization covered the fullspectral range which includes the very rapid absorption atthe near-IR wavelengths, the coefficients and exponents inequation (8) are invariant and were determined from labo-ratory experiments using fresh water conducted in the early1900s. The ocean, however, contains salt and suspendedmatter. The coefficients and exponents in the 2-band param-eterization can be modified according to Jerlov water typeclassification [Jerlov, 1976], an obsolete index of oceanturbidity. It has been shown that variations in solar transmis-sion are explained almost entirely by upper ocean chlorophyllconcentration in the euphotic zone, cloud amount, and solarzenith angle [Ohlmann et al., 2000]. These factors are thebasis of the Ohlmann and Siegel [2000] parameterizationwhich is the only parameterization to claim to resolve solartransmission variations within the top few meters of theocean. Global remotely sensed chlorophyll maps replacethe crude use of Jerlov water types. It should, however,be mentioned that variations in chlorophyll concentrationare of little importance for radiant heating within the uppermeter because a significant amount of the total energyexists beyond the chlorophyll sensitive wave bands, asstated by Ohlmann et al. [2000]. In order to adopt theOhlmann and Siegel approach chlorophyll concentrationvalues are obtained from monthly mean SeaWiFS 9 kmchlorophyll-a climatologies. This data set has only beenavailable since September 1997 and hence could not beused in the studies at the mooring sites. Tests were carriedout and the Ohlmann and Siegel parameterization togetherwith SeaWiFS data was found to slightly improve RMSerrors and reduce extremes when compared with the 9-bandparameterization.[47] The modeled diurnal temperatures can only be

validated by comparing with individual satellite SST obser-vations through the day. For this reason it is essential thatthe model starts from accurate initial temperatures, other-wise the model-observation differences will be characteris-tic of any initial offset rather than differences developingthrough the day. The GOTM initial profiles are obtainedfrom the UKMO operational ocean prediction system,


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FOAM [Bell et al., 2000], valid at 00:00 UTC each day,modified by OSTIA SSTs throughout the mixed layer togive a nighttime representation as close as possible to theexpected conditions.

[48] The work presented here is based in the AtlanticOcean and therefore 00:00 UTC always represents a night-time temperature (otherwise a local time correction would

Figure 3. Maps of the Atlantic Ocean showing daily mean wind stress (t) and diurnal warming of SST(Dq0.015m) for 1–7 January 2006.


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be needed). Details of this procedure are provided byPimentel [2007].

5. NWP-Based Predictions

5.1. Modeled Diurnal Cycles

[49] The optimized modeling arrangement incorporatingIW mixing, a dynamically calculated air-sea flux, and aSeaWiFS-based solar penetration, was implemented overthe Atlantic Ocean (50�S to 50�N and 270�E to 359�E) on a1� latitude and longitude grid. Modeled diurnal variability(Dq0.015m) maps were produced for the first week ofJanuary 2006 and are shown in Figure 3. Also shown inFigure 3 for comparison are graphs of the daily mean windstress (t).[50] The pattern of the modeled diurnal warming signals

shows significant variability on a day to day basis. Thesechanges closely follow the shifting wind stress patterns,with areas of low wind stress resulting in stronger diurnalwarming. This particular period is during southern hemi-sphere summer and several places south of the equator reacha peak SWR of 1000 W m�2. However, these areas of highpeak SWR are interspersed with areas of low peak SWR,around 500 W m�2 because of cloud cover (as determinedfrom the ECMWF analyses). The results suggest that themajority of the Atlantic at this time experiences low diurnalwarming, between 0 and 1�C, although some areas, pre-dominately in the southern (summer) hemisphere, show adiurnal warming of above 1�C. There are also small areaslocated mainly in the latitude band 40� to 20�S where thediurnal signal becomes much larger, 2–4�C. Areas of lowand extremely low, <0.01 Nm�2, wind stress appear to befairly good indicators of these regions of diurnal warming.The strongest diurnal warming signals only occur whenvery low wind stresses coincide with very strong SWR.[51] The area of the most significant and frequent

diurnal warming is in the latitude band 40� to 20�S. Thesusceptibility of the latitude band 40� to 20�S to intensediurnal warming during January has been noted before[see Stuart-Menteth et al., 2003, Figures 1 and 4] although

the intermittent nature of the warming pattern is apparent. Aparticular area can experience very strong diurnal warmingone day and then the next day experience negligible diurnalwarming as weather systems come and go. For example inFigure 3 on the 2 January 2006 centered at (38�S, 340�E)there is a small pocket of strong diurnal variability sur-rounded by stronger wind stresses resulting in low diurnalwarming. This pattern can be followed in the subsequent daysas the weather system moves east and dissipates. In the wakeof the strong winds are areas of calm resulting in moderate tostrong diurnal warming signals.

5.2. Satellite Validation

[52] To assess the accuracy of the modeled diurnal warm-ing estimates, GHRSST L2P observations from SEVIRI,AMSR-E, and TMI are compared to hourly model output.The results presented in Table 4 show that overall (3rd fromlast row) the model-observation differences have a mean biasof 0.09�C, a standard deviation (STD) of 0.54�C, and anRMS (error) of 0.56�C. Very little bias is seen for SEVIRI,and a slight positive bias, cooler observations than model, forAMSR-E and TMI. This could represent an inherent cool biasin AMSR-E and TMI measured SST compared with theSEVIRI SST.[53] Table 4 also shows that, like the mean, the STD and

the RMS errors for SEVIRI are much smaller than the otherobservation types. This indicates a much smaller variablecomponent to the SEVIRI matchup errors. The overall

Table 4. Comparing Model Output, q0.015m, Against GHRSST

L2P Satellite Data (SEVIRI, AMSRE, and TMI) for the Atlantic

Oceana

Matchup Number Mean SD RMS

GOTM-SEVIRI 28,075 0.01 0.35 0.35Day: GOTM-SEVIRI 7610 �0.02 0.32 0.33Night: GOTM-SEVIRI 6264 0.01 0.36 0.36GOTM-AMSRE 26,884 0.13 0.59 0.62Day: GOTM-AMSRE 6009 0.14 0.51 0.55Night: GOTM-AMSRE 5660 0.19 0.55 0.61GOTM-TMI 22,269 0.16 0.64 0.68Day: GOTM-TMI 6103 0.15 0.64 0.67Night: GOTM-TMI 4647 0.07 0.66 0.67GOTM-All 77,228 0.09 0.54 0.56Day: GOTM-All 19,722 0.08 0.51 0.52Night: GOTM-All 16,571 0.09 0.54 0.55

aArea of comparison was 50�S to 50�N and 270�E to 359�E during 1–7January 2006. Results show number of matchups, mean, standard deviation,and root mean square difference; values in �C. GHRSST, Global Ocean DataAssimilation Experiment High-Resolution Sea Surface Temperature; L2P,Level-2 Preprocessed; SEVIRI, Spinning Enhanced Visible and InfraRedImager; AMSRE, Advanced Microwave Scanning Radiometer-EOS; TMI,Tropical Rainfall Measuring Mission Microwave Imager; GOTM, GeneralOcean Turbulence Model.

Table 5. Comparing OSTIA to GHRSST L2P Satellite Data for

the Atlantic Oceana

Matchup Number Mean STD RMS

OSTIA-SEVIRI 28,447 �0.14 0.31 0.36Day: OSTIA-SEVIRI 7693 �0.14 0.27 0.33Night: OSTIA-SEVIRI 6376 �0.12 0.32 0.36OSTIA-AMSRE 27,364 �0.03 0.55 0.55Day: OSTIA-AMSRE 6068 0.06 0.48 0.49Night: OSTIA-AMSRE 5803 �0.03 0.60 0.60OSTIA-TMI 23,750 �0.01 0.65 0.65Day: OSTIA-TMI 6137 0.05 0.60 0.60Night: OSTIA-TMI 5382 �0.20 0.72 0.78OSTIA-All 79,561 �0.06 0.52 0.53Day: OSTIA-All 19,898 �0.02 0.48 0.48Night: OSTIA-All 17,561 �0.11 0.57 0.59

aArea of comparison was 50�S to 50�N and 270�E to 359�E during 1–7January 2006. Results show number of matchups, mean, standard deviation,and root mean square difference; values in �C. OSTIA was used as theinitial condition for the Atlantic model runs. OSTIA, Operational SeaSurface Temperature and Ice Analysis.

Table 6. Comparison of GOTM and OSTIA Against GHRSST

L2P Satellite Data for the Atlantic Oceana

Matchup Number Mean STD RMS

GOTM-SEVIRI 3115 0.20 0.55 0.59GOTM-AMSRE 2809 0.51 0.89 1.03GOTM-TMI 3149 0.33 0.91 0.97GOTM-All 9073 0.34 0.81 0.88OSTIA-SEVIRI 3115 �0.29 0.52 0.59OSTIA-AMSRE 2809 �0.16 0.76 0.77OSTIA-TMI 3149 �0.49 0.88 1.01OSTIA-All 9073 �0.32 0.74 0.81

aArea of comparison was 50�S to 50�N and 270�E to 359�E during 1–7January 2006 when the modeled diurnal warming magnitude was greaterthan 1�C. Results show number of matchups, mean, standard deviation, androot mean square difference; values in �C.


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model-observation differences are shown to be similar fordaytime and nighttime matchups and the RMS and STD varyby only 0.03�C. This does suggest that this diurnal model isable to give as good a match to the satellite measurementsduring the day as during the night. Daytime here is defined asoccurring between the restricted hours 10–16 (local time),and nighttime hours between 22–04 (local time). The modelis initialized to OSTIA between the stated nighttime hours.[54] The satellite observations are also compared directly

to the OSTIA combined SST product. Technically OSTIAapplies a sensor specific bias correction before it ingestsobservations [Stark et al., 2007], which is designed to takeaccount of atmospheric phenomena, such as aerosols anddust. In Table 5 the satellite observations all have a negativebias (with only two exceptions), showing that the satelliteobservations are slightly warmer than OSTIA on average.This should be expected as OSTIA represents an estimate ofthe foundation SST, i.e., the ocean temperature at a depthwhich is free of diurnal variations, whereas the matchupshere compare all observations, including those that contain adiurnal signal. Although the fact that larger negative biasesare found during the nighttime than the daytime for theAMSRE and TMI cases suggests that other factors are alsoimportant, notably that OSTIA uses other additional obser-vations and these will have an influence on the biases.When compared to the GOTM-observation comparisons inTable 4 we see that the negative biases are no longerwidespread, i.e., GOTM is warmer than OSTIA. TheGOTM model is shown to improve on the OSTIA whencomparing with SEVIRI data alone. The model is reducingthe mean error by removing a bias due to diurnal warming(although this bias may be slightly overestimated by themodel). This in turn is decreasing the RMS error, but it isslightly increasing the scatter as seen in the STD, whichmay be due to the coarse resolution meteorological forcing.The advantage of modeling the diurnal cycle over persis-tence then would be that more observations (i.e., includingthose taken during low wind speed days) could be included

in the analysis with little or no increase in variability. Itappears that SEVIRI observations are much more sensitivein picking up diurnal warming than either AMSRE andTMI, thus the much closer correspondence of SEVIRI inboth mean and RMS to the diurnal model. This could bebecause the SEVIRI observations have a finer spatialresolution, 0.1�, compared with AMSRE or TMI, 0.25�,as well as other potential factors such as a lower base sensoraccuracy and the timing and temporal resolution of themeasurements. The model also performs better than OSTIAduring the nighttime only comparisons, demonstrating thesuccess of modeling the cooling phase of the diurnal cycle.However the model has a slightly larger mean difference toOSTIA during the daytime only comparisons, this is becauseof the cancellation of OSTIA warm errors relative toAMSRE and TMI, and cold errors relative to SEVIRI.SEVIRI is marginally warmer than the model for the daytimeonly comparison, supporting the case that the SEVIRI dataproduct records a stronger diurnal cycle than AMSRE orTMI.[55] To further assess the model we limit the comparisons

to occasions when the modeled diurnal warming magnitudeis greater than 1�C. This subset represents 9% of the totalnumber of cases considered above. The results of theseassessments are presented in Table 6. As before we noticethat the GOTM–SEVIRI errors in mean, STD, and RMS aremuch lower than the other observation types. The biasdifferences between GOTM and OSTIA are clear, with anegative bias for OSTIA (observations warmer on averagethan OSTIA) and a positive bias for GOTM (observationscooler on average than GOTM). GOTM performs better thanOSTIA when comparing SEVIRI and TMI, with a smallermagnitude in mean error and lower RMS errors. The largenegative biases against OSTIA indicate that strong diurnalwarming is occurring on these occasions; however, thepositive biases against GOTM suggest that the model mayhave a tendency to over estimate this diurnal cycle. As notedearlier, there is also the strong possibility that TMI andparticularly AMSRE may not be picking up warming signalsas clearly as SEVIRI. In Figure 4 the RMS errors are plottedthroughout the day. The RMS values seem to peak around16:00/17:00 UTC, with SEVIRI differences consistentlylower than AMSRE and TMI. Observation gaps between08:00–13:00 UTC and 20:00–24:00 UTC exist for AMSREand this also effects the AMSRE matchups in Table 6.[56] Further work is needed to understand and distinguish

between various sources of error in the observations and themodel so that maximal information content can be acquiredfrom the satellite measurements.

6. Discussion and Conclusions

[57] Progress has been made in understanding and advanc-ing the ability to numerically model diurnal variability of thenear-surface ocean. A widely used one-dimensional mixedlayer model, GOTM, is optimized for the purpose of diurnalcycle modeling using state-of-the-art parameterizations forair-sea flux and ocean radiant heating. It is tuned againsthigh-frequency observations from buoy data at three differentsites representing a range of ocean and meteorological con-ditions. It is demonstrated that diurnal warming estimates canbe reasonably reproduced at these buoy sites using only

Figure 4. Hourly, time from initialization, root meansquare differences between model output and satelliteobservations. This only considers cases where the modeleddiurnal warming was greater than 1�C and covers the region50�S to 50�N and 270�E to 359�E for 1–7 January 2006.


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6 hourly data, suggesting that 6 hourly NWP data could beused in determining diurnal cycles over wide areas.[58] The study of Bernie et al. [2005] found that to

capture 90% of the diurnal variability at the COARE sitea 3 hour or better temporal resolution was required. Whilethis result seems generally consistent with our findings inTable 3 the outlook is much more optimistic for the othersites studied here, where the 6 hour temporal resolutioneasily captures 90% of the diurnal variability. Major differ-ences between the methods used in this work and that ofBernie et al. [2005] should be noted. These include the useof a different definition of diurnal variability, an alternativeair-sea and radiative flux set-up, as well as differing mixingand solar penetration parameterizations.[59] A grid of 1-D GOTM models were run over a wide

area of the Atlantic ocean forced by NWP data, and theresults used to produce daily spatial maps of the diurnalwarming signal in SST. This mesh of models forced withNWP data is shown to be a very useful method, viz, inidentifying areas of diurnal warming and quantifying diur-nal signals in observational SST data. The magnitude andspatial distribution of diurnal SST signals are shown to havevariability on a day to day timescale. The resulting diurnalwarming maps are of interest in building a climatology ofthe magnitude and extent of diurnal cycles in SSTs, and assuch further our understanding of ocean-atmosphere inter-action. For a weeklong period over the Atlantic Ocean acomparison between a combination of IR and MW satellite-derived SST observations and the modeled diurnal cyclesresulted in a mean bias of +0.09�C and a STD of 0.54�C.[60] Maps, such as Figure 3 based on NWP model output,

can provide useful information in several ways. They can beproduced globally on a daily basis, as they do not rely onparticular overpass paths and times or the availability ofday/night overlaps in satellite observations. Second, manyclimate and ocean modelers are reluctant to include adiurnal cycle in their models because of the increased costof extra vertical resolution, therefore the satellite commu-nity need to provide observations for assimilation that arenot contaminated by a diurnal signal. These maps can beused either to flag observations likely to have diurnalwarming, or better still, model output could be used toremove the diurnal bias. Third, this model approach couldpotentially be useful for improving accuracy in observa-tional foundation SST products, again by removing thediurnal signal and reducing bias.[61] The different nature of SST observations and their

model counterparts, is highlighted, as well as the lack ofGCM model representations of diurnal variability. Differentapproaches are possible to the assimilation of SST intooperational oceanography models. An observation operatorcould be used to transform model variables of surfacetemperatures at depth and foundation SSTs into the skinand subskin temperatures of satellite measured SSTs. Alter-natively for producing foundation SST observational prod-ucts SST observations ‘corrupted’ by a diurnal signal needto be converted to the base temperature from which thediurnal thermocline has developed. A 1-D model equippedwith fine near-surface resolution and diurnal forcing, asdeveloped here, could be used as an effective dynamicobservation operator for the uses outlined above.

[62] These developments in diurnal SST modeling arebuilt on in a separate paper [Pimentel et al., 2008] thatdescribes a novel data assimilation method utilizing diurnalsignal information in satellite-derived SST observationstogether with the modeled diurnal SST to further reduceuncertainties in diurnal warming estimates.

[63] Acknowledgments. This study is funded by the U.K. NaturalEnvironment Research Council through the Data Assimilation ResearchCentre.

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��K. Haines, Environmental Systems Science Centre, University of

Reading, Harry Pitt Building, 3 Earley Gate, Reading RG6 6AL, UK.([email protected])N. K. Nichols, Department of Meteorology, University of Reading,

Whiteknights, Reading RG6 6AX, UK. ([email protected])S. Pimentel, Department of Earth Sciences, University of Simon Fraser,

8888 University Drive, Burnaby, BC V5A 1S6, Canada. ([email protected])


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modeling the diurnal variability of sea surface temperatures · s. pimentel,1 k. haines,2 and n. k....

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