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1 Title: Profiles of Ocean Heating (POSH): a new model of upper ocean diurnal thermal variability Running title: POSH: a model of diurnal thermal variability Chelle L. Gentemann 1,2, Peter J. Minnett 2, and Brian Ward 3 1 Remote Sensing Systems 438 First St. Suite 200; Santa Rosa, CA 95401; (707) x14; gentemann@remss.com 2 University of Miami, Rosenstiel School of Marine and Atmospheric Science, 4600 Rickenbacker Causeway; Miami, FL 33149; (305) ; pminnett@rsmas.miami.edu 3 Old Dominion University, Department of Ocean, Earth and Atmospheric Sciences, nd St., Norfolk, USA; (757) ; bward@ccpo.odu.edu Paper Index Terms: 0438, 4504, 4572 Paper Key Words: Diurnal, Sea Surface Temperature I use *** in document where there are things that need to be addressed. You can search for *** to find specific comments. I don t mean in any way to restrict comments or contributions to just areas with ***. Please feel free to comment & suggest throughout document. 1

2 Abstract Radiometric measurements of the ocean surface diurnal warming and state-of-the-art profiles of the upper ocean are utilized to assess the temporal and vertical variability of diurnal warming and to develop a new physics-based model of near-surface diurnal warming. The in situ data and model simulations will be inter-compared, with the goal of comprehensively evaluating differences between the data and model results. Based on these results, the model will be refined, while attempting to maintain agreement with the in situ measurements. The new model provides a straightforward methodology for modeling the differences, due to diurnal warming, between measurements made at different depths (1 m in situ, 1 cm microwave, and 10 µm infrared). These results will have direct application to the GODAE requirements and the results will be useful in providing insight into the physical processes in the upper ocean. This will lead to furthering SST product development and more confident use over a broad spectrum of applications. 1 Introduction There is increasing interest in including satellite-based retrievals of SSTs in the historical record for climate applications. Satellite data can provide much needed measurements in remote regions. These data often lead to an improved knowledge of the spatial and temporal structure of seasonal and inter-annual variability and a reconstruction of global SST. NWP, climate, mesoscale oceanography requires remotely sensed SSTs with accuracy of K [GOOS, 1999]. Since diurnal warming of the ocean surface can reach amplitudes of 3.0 K or more, an improved understanding of diurnal warming is necessary to meet these temperature accuracy requirements. Additionally, since diurnal warming affects the upper ocean surface, which is in direct contact with the atmosphere, improved estimates of diurnal warming, will lead to better estimates of air-sea heat and gas fluxes. Failing to account for a diurnal cycle in Sea Surface Temperatures (SSTs) leads to errors in determining surface fluxes for numerical weather prediction (NWP) and climate models [Webster et al., 1996;Woods et al., 1984]. Tropical atmospheric circulation is sensitive to relatively small changes in SSTs [Palmer and Mansfield, 1984;Shukla, 1998] as is local atmospheric convection [Chen and Houze, 1997] and SST variability in this region is important to understanding climate change. The Global Ocean Data Assimilation Experiment (GODAE) SST science team has initiated an international effort to parameterize the upper ocean thermal structure with the goal of blending SST retrievals made at different depths and different times of the day. While this effort is not specifically aimed towards providing a climate-quality data set, concerns of climate scientists are being addressed. At a GODAE High-resolution SST (GHRSST) workshop, the magnitude of diurnal warming present in current SST analyses was discussed in detail [Donlon, 2002b]. It was agreed that future global SST products should provide a foundation SST, defined as the SST without any diurnal warming. It is perhaps the SST most representative of the temperature of the ocean mixed layer, but will appear to be slightly cooler when measured by infrared (IR) radiometers due to the skin effect. To determine this foundation SST, it is necessary to estimate diurnal warming and removed the warming from daytime SST retrievals. 2

3 2 Background The upper ocean is heated by solar radiation and in low-wind conditions may form a diurnal thermocline. A shallow thermally stratified layer, commonly referred to as the cool skin layer, exists at the air-sea interface. Within this thin layer molecular forces dominate and molecular conduction is the primary mechanism for heat transfer. This skin-layer sits passively on top of any warming or cooling within the upper ocean and is responsible for a small difference ( K) between the skin and sub-skin temperatures. Directly below the skin layer, the temperature is referred to as the sub-skin temperature and is often equal to the mixed layer temperature. The upper ocean layer is usually referred to as the mixed layer because turbulence often results in a wellmixed layer with little stratification. Often, this layer is not well mixed as stratification may be introduced either by solar warming or precipitation, creating vertical temperature and density gradients. Thermal stratification established by solar heating is referred to as a diurnal warm layer or diurnal thermocline. Vertical temperature gradients within the diurnal thermocline, Figure 1, are determined by the absorption of radiation at differing depths (determined by the absorptivity of the water), the vertical diffusion of heat, the vertical stratification in the upper ocean mixed layer, and the rate of turbulent mixing within the mixed layer. After sunset, the surface layer cools as the ocean loses heat to the atmosphere and space. The cooler, denser water at the surface is gravitationally unstable and results in free convection, overturning the mixed layer and causing the layer to deepen and temperature gradients to diminish. Stratification also may be decreased by surface wind stress-induced mechanical mixing of the upper ocean, by shear-flow instabilities, or by breaking internal waves. The diurnal thermocline has been studied surface measurements, profile measurements of the upper ocean, and theoretical modeling. 2.1 Diurnal thermocline measurements Diurnal thermoclines were first recognized in 1942 [Sverdrup et al., 1942] and have been studied extensively since [Defant, 1961;Donlon, 2002a;Fairall et al., 1996;Schluessel et al., 1990;Woods and Barkmann, 1986]. Surface temperature deviations greater than 3.0 K, referenced to subsurface temperatures below the extent of surface heating are not uncommon [Minnett, 2003;Yokoyama et al., 1995] and may persist for hours. Most research into diurnal thermoclines has utilized sub-surface temperatures. Determining how the ocean surface diurnal heating responds to variability in forcing has been primarily addressed through theoretical modeling or extrapolation of results from in situ (buoy) measurements measured 0.5 m to 1.5 m below the skin layer. The diurnal heating signal at the ocean surface may be quite different than heating at 0.5 m as the skin layer responds very rapidly to changes in heat and momentum Surface measurements The largest number of measurements and broadest geographical sampling are from satellite retrievals of SST. These observations are a snapshot of warming, usually lacking detailed radiative and surface stress forcing histories that are needed to understand the magnitude of warming. They facilitate insight by providing skin and sub-skin SST data and a significant understanding of the distribution and general magnitude of warming is possible. Geo-stationary satellites provide hourly measurements but calibration problems have limited their utility for diurnal studies.[wick et al., 2002] In situ skin SST data provide another data source for examining diurnal warming at the ocean surface. The in 3

4 situ data have a significant advantage over satellite data because the data are usually taken from research vessels with a suite of meteorological and oceanographic instrumentation that measure many relevant parameters. They are invaluable in examining the temporal decorrelation of warming with radiative or surface stress forcing, but the limited sampling must be carefully considered. The Marine-Atmosphere Emitted Radiance Interferometer (M-AERI) is a sea-going modified AERI [Minnett et al., 2001] originally developed for the Department of Energy Atmospheric Radiation Measurement (ARM) program [Knuteson et al., 2004a;Knuteson et al., 2004b]. The instrument detectors receive radiation reflected by a scan mirror which views sky, sea-surface, and internal calibration reference blackbodies which are traceable to National Institute of Standards and Technology (NIST) standards [Rice et al., 2003]. SST is retrieved using sea and sky view data at 7.7 µm [Minnett et al., 2001]. The instrument enters a safe mode during rain to avoid contamination of the scan mirror. Data from four research cruises and the cruise ship Explorer of the Seas provides 72 days with clear diurnal warming. A detailed description of the data set and methodology for isolating diurnal variability from the cool skin layer and other effects is given in [Gentemann, Chelle L. and Minnett, Peter J., submitted.]. As detailed in Gentemann and Minnett [submitted.], these data show that the surface signature of diurnal warming is primarily related to wind speed and secondarily to insolation. Small changes in wind speed (< 1.0 ms -1 ) rapidly and strongly affect the amplitude of diurnal warming present in the sea surface. On the majority of days, the diurnal peak was not coincident with the insolation peak, but instead directly related to the minimum wind speed during the day, causing the time of the peak to shift depending on when the minimum winds occur. Fluctuations in wind speed can result in multiple local peaks in diurnal heating. Above 6 ms -1, warming may become negligible in as quickly as 30 minutes Profile measurements Over 12 days, during the Barbados Oceanographic and Meteorological Experiment (BOMEX) [Delnore, 1972] acquired temperature and salinity profiles were made in the upper 50 m of the ocean. Five ships, each carrying an Eppley pyranometer, were stationed near Barbados making over 300 profiles of the upper ocean with Bissett Berman salinity-temperature-depth (STD) profilers. Each day, profiles were taken at the same time. Surface winds were reported as ms -1 for the first few days (20-26 June) and increased afterwards, eroding the diurnal warming. These first six days were used to examine the depth dependence of diurnal variability. Figure 1 shows the average profile for the R/V Discoverer over all six days at the various profile observation times. In Figure 1, Period A the formation of a warm layer of ~0.6 K with a thickness of 18 m is present by 11:00 LMT and a more stratified, warmer layer of ~1.6 K that then linearly decreases in temperature with depth to ~20 m develops by 14:00 LMT. As the surface cools, the profiles at 17:00 LMT are well mixed with a warm layer of ~1.1 K and a thickness of ~ 20 m. Profiles slowly relax to the original mixed layer temperature. In Period B the observed warming is always well-mixed within the warm layer and the linear gradient seen at 14:00 LMT in Period A does not occur, likely because of the higher wind speeds during this observation period. Data from the R/V Oceanographer is shown in Figure 2. In Period A, the warm layer is still well mixed above ~10 m, but becomes shallower and larger throughout the day. By contrast, the Period B observations had a warm layer well mixed down to 18 m. While the Delnore [1972] results are mainly 4

5 concerned with calculating the heat content and evaporation rates, these early profiles of diurnal warming point towards a family of curves for the growth and decay of warming within the mixed layer that is likely dependent on the history of radiative heating and turbulent mixing either through stress or shear-induced instabilities. Further profiles of diurnal warming [Halpern and Reed, 1976] were observed off the Northwest African coast during March 1974 during a period of very light winds (~2 ms -1 ). Measurements of radiation, air temperature, humidity, and wind speed were taken from the NOAA R/V Oceanographer. A buoy was fitted with 10 thermistors within the upper 24 m of the ocean. Hourly averages of the thermistors show the diurnal temperature range (Figure 4), diurnal amplitudes of 0.9 K to 1.4 K were found during the three days of the experiment and an exponential decrease in temperature with depth was observed (note the logarithmic scale in temperature). More recently, the vertical distribution of diurnal heating in the upper ocean was examined using Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment (TOGA COARE) profiles [Soloviev and Lukas, 1997]. Thirty-five profiles were taken as part of the TOGA COARE experiment in the Pacific, and it was found that often at low-wind speeds, the large diurnal signals were trapped in the top 1 m of the ocean, and at very low-wind speeds confined to the upper 10 cm. Profiles shown by Soloviev and Lukas [Soloviev and Lukas, 1997], Figure 5, have three distinctive vertical distributions of warming. Profiles taken at wind speeds greater than 7.0 ms -1 are well mixed, with diurnal warming less than 0.2 K with a warm layer depth of m. The ten profiles taken during wind speeds of ~2.0 ms -1 (B) have an almost constant warming ( K) down to slightly different depths (1-7 m), a decrease in the mixed layer temperature, and then constant (mixed layer) temperature below the warm layer. As pointed out in the paper, these profiles all have almost the same amount of warming at the surface, but the warming extends to very different depths. These profiles could best be estimated by a Gaussian shape with depth. The five profiles taken in calm weather (winds less than 2.0 ms -1 ) have warming confined to the upper meter and a very large surface warming of 3.0 K. These profiles appear to have an exponential decrease in temperature with depth. During TOGA/COARE upper ocean profiles of temperature were taken with the SILVERFISH instrument on rd the R/V Franklin [Webster et al., 1996]. Figure 6(a) shows the profiles taken on two different days. Figure 6a shows profiles from 13 January 1993, a day with strong insolation and light winds that result in a diurnal warm layer of ~2.0 K at the surface, diminishing exponentially with depth. Figure 6(b) shows profiles on 4 February a day with strong winds and weak insolation resulting in a well mixed, upper layer with no surface diurnal warming. In Figure 6(a), the base of the diurnal layer appears to be at about 2 m depth. These measurements suggest an exponential profile of temperature with depth at very low wind speeds when there is little mechanical mixing of the ocean and the heat is trapped at the surface, a Gaussian shape at mid-range ( ms -1 ) where some windinduced mixing deepens the warm layer, and then a smooth transition to a well-mixed layer at higher wind speeds. More recently, state-of-the-art instruments such as the Skin Depth Experimental Profiler (SkinDeEP) [Ward and Minnett, 2001] are able to provide more detail about the vertical structure than moored buoy arrays at discrete depths, neither observation gives us 5

6 an understanding as to why the observation is changing or information on the horizontal structure of turbulent mixing. Vertical profiles of upper ocean temperature from the SkinDeEP profiler are shown in Figure 6. In this example, the warming is mainly confined to the upper meter of ocean. There is a short decrease in insolation near the second tick on the x-axis (a cloud passed over) and the warm layer rapidly responds as the diurnal heating is quickly erased. After the cloud passes, the warm layer is rapidly reestablished. There is a large amount of variability in the amount, depth, and vertical distribution of diurnal heating. Thus, it is difficult to determine exactly what is being measured: local diurnal variability, non-local variability, or a sampling artifact. **brian any more here?*** 2.2 Modeling The Price, Weller, Pinkel (PWP) model [Price et al., 1986] uses surface fluxes and vertical profiles of temperature, salinity, and velocity. Within the mixed layer, the model mixes surface fluxes down until there is convective stability and the bulk (mixed layer stability) and gradient (shear flow stability) Richardson numbers are stable. Another model developed by Large et al. [Large et al., 1994] uses a K-profile mixing parameterization (KPP) to determine vertical mixing. These models have been extensively tested and compared to in situ measurements under light to moderate wind conditions [Anderson et al., 1996;Cronin and McPhaden, 1997;Fairall et al., 1996;Shinoda and Hendon, 1998;Webster et al., 1996;Weller and Anderson, 1996]. While often able to accurately reproduce diurnal warming, these diurnal models are difficult to implement over large regions where accurate estimates of radiation, sensible heat, latent heat, fresh water, and momentum surface fluxes, and vertical profiles of temperature, salinity, and velocity are not usually available. These difficulties have led to interest in developing simplified models of diurnal warming that utilize readily available data. Several simplified empirical models of diurnal warming, based on in situ and satellite data, have been developed. The first generation of empirical models attempted to calculate the peak warming [Kawai and Kawamura, 2002;Lukas, 1991;Webster et al., 1996]. The next generation of models attempted to calculate diurnal variability throughout the day [Gentemann et al., 2003;Stuart-Menteth et al., 2005]. While all these models are applicable in some situations, only the last two, are designed for application in a Near-Real Time (NRT) satellite analysis where measurements may occur throughout the diurnal cycle. Older models do not adequately describe the variability in diurnal warming, due to variable wind and insolation, present within a single day. The more recent models also have problems. Neither account for the changing length of the day, and the Gentemann model has no wind or insolation history and only responds to instantaneous values of surface wind speed. The Stuart-Menteth model includes four daily values of wind speed and two values of insolation. While including wind history and insolation history should lead to an improved model of diurnal amplitudes, it is likely that diurnal amplitudes are more affected by a more recent history (a few tens of minutes), rather than the 6-hour NWP fields. Rather than pre-determining a number of shapes, it may be more accurate to simply interpolate NWP wind fields throughout the day to estimate the diurnal shape. 6

7 The empirical models only return warming at the surface, only two models provide intra-day variability of warming, and only one attempts to include wind and insolation history. We are not aware of any inter-comparison of the empirical models or validation of the models at the ocean surface using in situ skin SST measurements. The bulk models provide estimates of the surface warming using integrated surfaces fluxes but have pre-determined linear vertical profiles of temperature. The more complicated turbulence closure models return temporally variable vertical structure which is important to understand how these warm layers interact with the mixed layer but are computationally intensive. Additionally, there has been little validation of the bulk or turbulence closure models at the ocean surface using in situ skin SST measurements. This research will aim to improve an established bulk model through better physical parameterizations determined through comparison with in situ measurements and develop a methodology for providing turbulence-closure-like vertical structure within the warm layer Fairall model The F96 diurnal model is based on the PWP diurnal model which, in turn, is based on the dynamical instability model of [Price et al., 1978]. The one-dimensional bulk model assumes that the diurnal layer is non-interactive with the mixed layer and assumes that the mixed layer is well-mixed with very small vertical gradients. The model determines the diurnal warming as the summation of vertical mixing and radiation processes driven solely by local surface fluxes of heat and momentum [Niiler and Kraus, 1977]. The model is developed from the one-dimensional heat equation. Surface values are assumed to be known, as the surface flux is equal to the total radiative flux, the freshwater flux is equated to evaporation and precipitation, and the surface stress is entirely wind driven: The radiative heating within the warm layer is the difference between the total heat loss (at the surface) and the solar insolation absorption within the warm layer. The model is based on dynamical instability model of Price et al. [1978] and has three requirements: static stability, mixed layer stability, and shear flow stability. The F96 version [Fairall et al., 1996] simplifies the PWP model by making the assumption that there is a linear gradient in temperature through the warm layer, which will always satisfy the first PWP criterion for static stability. The model also requires mixed layer stability but does not require the shear flow stability. F96 determined the diurnal heating at the surface as: T w 2Q ac =, [1] ρc D p T where the integrated radiative fluxes, Qac, at each time step Δ t, are: Q = Q + ( f ( D )* Q Q ) Δt, [2] ac ac w T sw r fw( D T), is the absorbed shortwave radiation, and the warming is confined to a depth, D T, determined by requiring the bulk Richardson number to be equal to 0.65: 7

8 D T 2R i ρc p τ ac =, [3] α g Q ac where the integrated wind stress energy, τ ac, is: and surface stress is: τ ac = τac + τt-1δ t, [4] τ = ρ u 2. [5] a * In the model, the net longwave is calculated: Q 4 = ε ( σ T Q ), [6] LW LW SB LW where ε LW is 0.97, the emissivity of the sea surface for longwave radiation, σ SB is Stephen-Boltzman constant, 5.67x10-8. The SST, T, and downwelling longwave, Q, are assumed to be known. Shortwave (solar) insolation is: where, r SW shortwave radiation, LW QSW = (1 rsw ) QSW, [7], the reflectivity of the sea surface for shortwave radiation is 0.055, and the QSW, is assumed to be known. Within the warm layer, the solar radiation is absorbed at depth using a 3-band exponential model of absorption: -z -z -z f ( z) = 1- ( (1- e ) (1- e ) (1- e )). [8] w The total radiative forcing within the warm layer is then: where the heat flux due to rain, does not collect data during rainfall. Q = Q f ( D ) ( Q + Q + Q + Q ), [9] tot SW w T LW sens lat rain Q rain, can be set to zero, since the M-AERI instrument 3 Results Extensive comparisons between the F96 model simulations and the M-AERI observed sub-skin diurnal warming revealed large differences. As discussed previously, the model development and previous validation studies have all utilized measurements below the sub-skin layer, at depths of 0.5 m and larger. These depths likely have a very 8

9 different response to fluxes of heat and momentum than the surface layer. The comparisons to sub-skin diurnal warming measurements lead to the development of a new model, based on the F96 model. The refinements and then the comparisons to M- AERI data are discussed in the next section. The model refinements were mostly based on the average diurnal warming for all 72 days (Figure 7). Improvements to the mean simulations for individual days were expected from this methodology, but improvements in the standard deviation of the difference between simulations and data were not guaranteed. The key differences when the observed diurnal warming was compared to the F96 diurnal simulations were (Figure 7A): F96 underestimated the amplitude of warming, the peak in warming occurred after the peak in data, warming persisted beyond observed warming in the afternoon, (Figure 7B): modeled warming underestimated amplitudes at low wind speeds and over estimated at high wind speeds, and (Figure 7C): warming was underestimated at high insolation. 3.1 Refinements to F96 The F96 model was refined here in several ways to improve simulations of the observed diurnal variability. The first modification to the model was to change the zeroing of accumulated heat and momentum from midnight to 6:00 LMT. The model includes no dissipation and so rapidly diverges from measurements due to the lack of viscous dissipation as well as any exchange of heat or momentum through the base of the warm layer. Accumulated momentum, heat, and diurnal warming were all reset to zero at midnight in F96, but since warming may persist well beyond midnight, this was changed to 6:00 LMT. This timing of minimum warming is consistent with the idea of a foundation temperature as introduced earlier. The parameterization of solar absorption within the diurnal warm layer was improved. The solar radiation absorption profile was changed from a 3-band spectral model to Simpson and Paulson [1981] model (Figure 8). The 9-band model has stronger absorption at all depths, but particularly at shallow layers and better captures the heating profile. The effect of solar angle was also included to better model the depth of radiation absorption. The new 9-band spectral absorption model: -z -z -z f ( z) = 1- (0.2370e * e e w -z -z -z x x e e e -z -z -z x x x e e e ). [10] This new spectral absorption model slightly improved the skill of F96 at lower wind speeds (when compared to M-AERI data) by increasing the simulated warming. Simulated warming was still low when compared to the M-AERI measurements; therefore the 9-band spectral model absorption was increased by 20%, for all wind speeds, determined by comparing the in situ measured diurnal amplitudes to the original model amplitudes. The total radiative forcing within the warm layer utilized in the new model is then: 9

10 Q = Q 1.2* f (cos( D )) ( Q + Q + Q + Q ). tot SW w T LW sens lat rain [11] While this increased the warming amplitudes slightly, the F96 model returns warming well beyond the observed in the late afternoon and evening. This was a result of the accumulated warm layer heat only decreasing through longwave radiation. The warm layer was assumed to be cut-off from the mixed layer. In reality, heat will be mixed down through viscous dissipation and through turbulent mixing across the base of the warm layer. Additionally, momentum will dissipate through viscous dissipation and turbulent mixing at the base of the warm layer. Using these arguments, dissipation of wind energy and heat was added to the model. The original model accumulated wind stress and total heat by adding wind stress and heat from the previous time step: τ = τ + τ Δt ac ac t-1 Qac = Qac + Qt-1 Δt. [12] The original equations were modified to dissipate the accumulated heat and momentum: τ = (1 εδ t) τ + τ Δt ac ac t-1 Q = (1 χδ t) Q + Q Δt, ac ac t-1 [13] where the dissipation rates of momentum,ε, and heat, χ, were determined by minimizing the standard deviation of the difference between the model and M-AERI data with variable dissipation of momentum and heat. Dissipation of momentum reduces turbulent mixing in the warm layer. This decreases the depth of the warm layer, increases stratification within the warm layer, and thereby increases the modeled surface warming. Conversely, dissipation of heat in the warm layer through exchange with the mixed layer increases the depth of the warm layer and decreases the modeled surface warming (Figure 11). The model with dissipation responded better to variations in surface stress and heat. Figure 11 shows a day where there were two measured peaks in warming (blue line) and illustrates how, by increasing the dissipation of momentum, the separate peaks are better represented. The original model with no dissipation of momentum resolves the first peak but does not resolve the second peak well, while the model with dissipation matches the variability seen in the measurements better. The bottom panel shows how the dissipation of heat in the warm layer reduces the late afternoon over-estimation of warming seen in the original model. While adding dissipation improved the F96 temporal response to solar heating and shear-induced mixing, the wind speed dependence did not match the measurements well. The original model underestimated warming at low wind speeds and overestimated warming at high wind speeds. It was determined that the F96 assumption of a linear profile of temperature within the warm layer would cause this result. The F96 assumed warming is a maximum at the surface and decreases linearly to zero at the base of the diurnal warm layer. Previous studies of upper ocean temperature profiles do not show a linear temperature increase in the warm layer, but instead an exponential and then, with 10

11 wind mixing, a constant mixed warm layer at the surface which then decreases at depth. At low wind speed the diurnal thermocline has minimal turbulent mixing, leading to strong stratification. The profile of absorption of shortwave radiation is exponential and it is therefore likely that the profile of warming has a similar shape. As wind increases, mixing in the warm layer will increase and the profile should relax towards vertical. The profile of upper ocean temperature within the diurnal thermocline is measured by SkinDeEP. ***short description of SkinDeEP here please*** SkinDeEP profiles of temperature through the diurnal thermocline are shown in Figure 9. Panel A shows data from several different stations with different wind and insolation histories. The groupings of curves shown in the figure are generally from different days. These data have been normalized by depth and heat content to illustrate the different profiles of warming at variable wind speeds. The lower wind speeds show an exponential decrease of warming with depth while higher wind speeds have a decreased gradient at the surface that then decreases at depth to zero, indicating more mixing in the upper surface. Panel B shows data from four different days, at insolation between 650 and 750 Wm -2. The panel clearly shows different temperature gradients for different wind speeds. The warming is not consistently decreasing with wind speed, likely because this is a snapshot of days with different wind and radiative fluxes. The profiles at 0-1 ms -1 (red lines) have an exponential decay of temperature with depth. As winds increase slightly, increases mixing in the upper layer causes the profiles at 1-2 ms -1 (orange lines) to bend back towards vertical in the top 0.25 m. At even higher wind speeds (green and blue lines) the profile takes on a non-exponential shape. The windinduced mixing results in an increasingly mixed diurnal thermocline, decreasing the temperature gradients, and the profile becomes more and more vertical. Panel C shows the same profiles, but normalized to mixed layer depth and normalized heat content. This illustrates a methodology to determine diurnal thermocline profiles based on determination of warm layer depth and magnitude. The wind speed dependence of these diurnal profiles was reproduced by a set of five equations, dependent on wind speed, with depth normalized by the diurnal warm layer thickness and normalized heat content: 2 9.5z 1 Δ T( z) = e for u 1.5ms 3 9.5z 1 Δ T( z) = e for u = 3ms 5 9.5z 1 Δ T( z) = e for u = 4.5ms 7 9.5z 1 Δ T( z) = e for u = 6ms 9 9.5z 1 Δ T( z) = e for u 7.5 ms. [14] The new temperature profiles (Figure 10) smoothly transition between the different equations as the wind speed changes. The F96 diurnal thermocline heat content is calculated using the original linear profile and F96 estimate of surface warming. At each time step, a profile is calculated, with the vertical axis scaled by the depth of the warm layer. The magnitude is adjusted so that the new profile and the original linear assumption have the same total heat content. In this way, the total heat is the same while the profile, and therefore surface expression of warming, is quite different. The profile 11

12 scales with the warm layer depth to ensure that it smoothly decreases to zero at the base of the warm layer. This refined F96 model, with dissipation, different shortwave absorption, and vertical structure is referred to as the Profiles Of Surface Heating (POSH) model hereafter. The dependence of diurnal warming on variations in wind speed, insolation, and time of day was explored for the F96 and POSH models. To determine the dependence on these forcing, the model simulations were evaluated for 24 hours with insolation was varied realistically through the day. The length of day was kept constant for all simulations; only the amplitude of insolation decreased. For each insolation factor, the model was evaluated with different constant (through the day) wind speeds. The 24-hour model was evaluated for peak insolation from 0 to 400 Wm -2 at increments of 1 Wm -2. Each of these simulations was evaluated for 60 wind speeds varying from.2 ms -1 to 11.8 ms -1 at increments of 0.2 ms -1. Figure 12 shows the dependence on wind speed and insolation at 14:00 LMT for both the F96 and POSH models. There is little warming above 6 ms -1 and below 80 Wm -2. The maximum warming is 5.4 K (F96) and 7.4 K (POSH). Figure 13 shows the temporal dependence of F96 and POSH on local time. The peak warming in the F96 model occurs at 14:00 LMT, 2 hours after the peak in insolation. In the POSH simulations, the added dissipation in heat has changed the temporal dependence to a less skewed shape that more closely resembles the actual insolation forcing, with the simulated warming peaks at 13:00 LMT. 3.2 Model evaluation The daily time series figures all have the same format. The top panel shows insolation in the background, wind speed (green line) axis on the right, diurnal warming (blue line) axis is on the left, F96 (grey line), and POSH (black line). All 72 days of diurnal warming in the data, the bias and standard deviation of the difference, modeled warming minus observed warming, from 6:00 LMT onwards, are shown in Table 1. In the bottom panel, profiles of the temperature within the diurnal thermocline, calculated by the POSH model are shown. For visualization purposes, the profile amplitude was normalized by the surface warming value and then multiplied by four times the time step. Therefore, the amplitude should be taken from the top panel, but the shape and depth of warming are correctly shown in the bottom panel. Before sunrise and after the diurnal thermocline has been erased, the temperature is constant with depth. Once a diurnal thermocline forms, the temperature profiles in the figures end at the base of the warm layer. All 72 days were examined closely, initially to determine where the F96 model succeeded and failed in modeling observed warming. These results lead us to the refinements implemented in POSH. The following section discusses six days with diurnal warming and the model simulations. In Figure 14, there were two peaks in diurnal warming, directly related to two decreases in wind speed. The peaks in warming occurred slightly after the local minimums in winds speed. The F96 model amplitudes were too low and temporally lag the observed peaks for both occurrences. Both peaks were well defined in the POSH simulation and the maximums in warming were close to the observed maximums. The warm layer was initially shallow, deepening with the increase in wind speed, and then decreasing in depth again as the wind decreases for the second diurnal peak. The temperature gradients in the diurnal thermocline are very large at low wind speeds and 12

13 decreased with increasing wind speed. From 14:00 15:00 LMT the wind speed was decreasing and the profile temperature gradient increased. Diurnal warming from 03 June 2002 (Figure 15) was variable, with two diurnal local maximums, the late afternoon peak larger than the morning peak. Variable cloud cover was present throughout the day. The F96 simulated warming under-estimated the peak, placing after the observed peak, then F96 overestimated warming in the afternoon. The POSH model correctly matched the timing and amplitudes of the observed two peaks. The warm layer remained relatively shallow and temperature gradients were strong from 9:00 to 11:00 LMT, when the wind speed was low. As the wind increased from 11:00 to 12:30 LMT, the diurnal thermocline deepened and the temperature gradients were decreased. From 12:30 to 17:00 LMT the wind decreased, the warm layer thinned, and gradients increased. Finally, after 17:00 LMT, the wind increased, the warm layer deepened, and gradients decreased, until the thermocline was ultimately erased after 20:00 LMT. 12 July 2002, (Figure 16) had clear skies (classical bell shaped insolation), strong insolation, and low wind speeds. The relatively constant, low wind speeds from early in the day through 12:00 LMT resulted in diurnal warming that closely echoed the slope of the increasing insolation. After 12:00 LMT, the winds slowly increased, decreasing the warming. The F96 simulated warming was too small, occurred after the observed peak, and had warming persist late into the evening, long after observed warming was negligible. The POSH model accurately simulates the observed warming until 12:30 LMT. The POSH model lagged the peak in warming by approximately an hour and then retained too much heat in the afternoon. Warming persisted in the POSH model until 19:00; approximately 2 hours after observed warming had disappeared. On 13 Feb 2003 (Figure 17) a mid-afternoon increase in wind speed from 14:00 to 15:30 LMT rapidly erased observed warming. The wind decreased for a short period at around 15:45 LMT, but radiative fluxes were small and the observed warming increased only slightly. Neither model simulation has the correct peak amplitude. The F96 model had about 50% less warming than observed, did not correctly resolve the peak, and did not diminish as quickly as the observed warming. The POSH model followed the observed warming more closely than the F96 model. It had too much warming around 11:00 LMT and then, although it did resolve the peak, not enough warming was simultated. The POSH model followed the observed decrease in warming closely. The low wind speeds result in very shallow and strong gradients of temperature in the warm layer that rapidly deepened and weakened with the increase in wind speed. A large peak in observed warming, followed by a sharp decrease was observed on 15 November 2001 (Figure 18). Neither of the models was able to accurately model the amplitude of the diurnal peak. The observed warming decreases within ten minutes of the increase in wind speed and the POSH model rapidly diminished alongside the data. The POSH amplitude was larger than that of F96, better matching the observed warming. After the increase in wind speed, there was no observable warming (after approximately 17:00 LMT), but the F96 model had warming persisting to almost 20:00 LMT. The thermocline depth increased rapidly after the increase in wind speed. Another large diurnal warming event with two peaks occurred on 11 November 2001 (Figure 19). Low wind speeds persisted through most of the day, increasing slightly after 13:00 LMT. Small fluctuations in wind speed resulted in two observed peaks. The 13

14 F96 model does not resolve the two diurnal peaks, the amplitude is less than the observed warming, and after a small increase in wind speed at 16:00 LMT, the simulated warming is larger than observed until 24:00 LMT. The POSH model closely followed the observed warming, resolved both peaks, and diminished in amplitude realistically. The low wind speeds resulted in a very shallow diurnal thermocline with a strong gradient in temperature. Figures are indicative of the results seen by examining all 72 days of warming. The F96 model consistently underestimated warming, did not respond rapidly enough to changes in momentum and radiative fluxes, and often had more warming than observed late into the evening. This behavior is likely more accurate for diurnal warming at depth rather than at the surface. The POSH model was specifically developed to model surface warming and throughout the studies it consistently models the diurnal amplitudes and variability more accurately than F96. Table 2 shows the bias and standard deviation of the F96 and POSH modeled warming minus the observed warming for all 72 days. Biases are approximately equal, 0.00 K and 0.01 K for F96 and POSH, respectively. The standard deviation shows the improvement in modeling accuracy with POSH (0.36 K) less than the F96 (0.42 K) error. 4 Conclusions Observations of diurnal warming at the ocean surface are only available from a small number of instruments. The M-AERI deployment on the Explorer of the Seas provides routine measurements of skin SST temperatures in the Caribbean Sea. Data have been accumulating since 2000 and now form a significant data set of meteorological and oceanographic measurements. Data from four additional research cruises with M- AERI measurements of skin SST in the Indian Ocean, Southern Ocean, Pacific Ocean, and Gulf of California were utilized. This is a unique data set of skin SST observations with the appropriate ancillary meteorological and oceanographic parameters necessary to investigate diurnal warming variability and model skill at the ocean surface. These data were utilized to develop a new model of diurnal variability. The F96 model was refined to improve performance when compared to the surface measurements of diurnal warming from M-AERI. Parameterization of the absorption of solar radiation was improved by using a 9-band spectral model with absorption increased by 20%. Dissipation of heat and momentum was added to the model to increase the model responsiveness to changes in surface heat flux and surface stress. Nondimensional profiles of warming that are dependent on wind speed were added to the model. The profiles scale by the model calculated heat content and warm layer thickness. At low wind speeds warming is concentrated at the surface. As wind speed increases and correspondingly the surface layer turbulent mixing increases, the profiles relax to a more vertical state expected of a more mixed diurnal warm layer. These profiles are returned with each time step in the model and provide an estimate of the vertical temperature structure within the diurnal thermocline. The POSH model appreciably increased the skill of its heritage model (F96) at simulating diurnal warming at the ocean surface. To understand intra-day variability, to estimate the heat available at the surface throughout the day, and to model diurnal warming sampled by measurements from geo-stationary or low-inclination orbiting satellites, the POSH model has the least error when compared to the M-AERI surface measurements of diurnal warming. 14

15 5 Acknowledgements We would like to acknowledge the contributions of Nick Shay, Ian Robinson, Bob Evans, and Eric Chassignet. The data for this study were collected by Eddie Kearns and Bob Evans (R/V Melville), Chip Maxwell, and Don Cucchiara (Explorer of the Seas), and Erica Key (R/V Ewing and R/V Aurora). This work was supported by funding from NOAA (NA030AR ), NASA (NM , NAG , NNG04HZ33C, and NAS ), and NSF ( ). ***Brian here maybe you want to add grant number and people on crusie?**** 15

16 References Anderson, S. P., R. A. Weller and R. B. Lukas, Surface buoyancy forcing and the mixed layer of the western Pacific warm pool: Observations and 1D model results, Journal of Climate, 9(12), , Chen, S. S. and R. A. Houze, Diurnal variation and lifecycle of deep convective systems over the tropical Pacific warm pool, Quarterly Journal of the Royal Meteorological Society, 123, , Cronin, M. F. and M. J. McPhaden, The upper ocean heat balance in the western equatorial Pacific warm pool during September-December 1992, Journal of Geophysical Research, 102(C4), , Defant, A., Physical Oceanography, Pergamon Press, Delnore, V. E., Diurnal variation of temperature and energy budget for the oceanic mixed layer during BOMEX, Journal of Physical Oceanography, 2, , Donlon, C. J., Proceedings of the Second GHRSST-PP workshop: "Removing Barriers to the Implementation of the GHRSST-PP, 2002a. Donlon, C. J., Report of the GHRSST-PP Science Team Meeting, Tokyo, Japan (May 13th 2002), 2002b. Fairall, C. W., E. F. Bradley, J. S. Godfrey, G. A. Wick, J. B. Edson and G. S. Young, Cool-skin and warm-layer effects on sea surface temperature, Journal of Geophysical Research, 101(C1), , Gentemann, C. L., C. J. Donlon, A. Stuart-Menteth and F. J. Wentz, Diurnal signals in satellite sea surface temperature measurements, Geophysical Research Letters, 30(3), 1140, Gentemann, Chelle L. and Minnett, Peter J., "In situ measurements of diurnal thermal variability", GOOS, Global Physical Ocean Observations For GOOS/GCOS - An Action Plan for Existing Bodies and Mechanisms, GOOS, Halpern, D. and R. Reed, Heat budget of the upper ocean under light winds, Journal of Physical Oceanography, 6, , Kawai, Y. and H. Kawamura, Evaluation of the diurnal warming of sea surface temperatures using satellite-derived marine meteorological data, Journal of Oceanography, 58(6), ,

17 Knuteson, R. O., H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short and D. C. Tobin, Atmospheric Emitted Radiance Interferometer. Part I: Instrument Design, Journal of Atmospheric and Oceanic Technology, 21(12), , 2004a. Knuteson, R. O., H. E. Revercomb, F. A. Best, N. C. Ciganovich, R. G. Dedecker, T. P. Dirkx, S. C. Ellington, W. F. Feltz, R. K. Garcia, H. B. Howell, W. L. Smith, J. F. Short and D. C. Tobin, Atmospheric Emitted Radiance Interferometer. Part II: Instrument Performance, Journal of Atmospheric and Oceanic Technology, 21(12), , 2004b. Large, W. G., J. C. McWilliams and S. C. Doney, Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization, Reviews of Geophysics, 32(4), , Lukas, R. B., The diurnal cycle of sea surface temperature in the western equatorial Pacific, 2, 1-5, Minnett, P. J., Radiometric measurements of the sea-surface skin temperature - the competing roles of the diurnal thermocline and the cool skin, International Journal of Remote Sensing, 24, , Minnett, P. J., R. O. Knuteson, F. A. Best, B. J. Osborne, J. A. Hanafin and O. B. Brown, The Marine-Atmospheric Emitted Radiance Interferometer (M-AERI), a highaccuracy, sea-going infrared spectroradiometer, Journal of Atmospheric and Oceanic Technology, 18, , Niiler, P. P. and E. B. Kraus, One-dimensional models of the upper ocean, Tarrytown, N.Y., Palmer, T. N. and D. A. Mansfield, Response of two atmospheric general cirulation models to sea-surface temperature anomalies in the tropical East and West Pacific, Nature, 310(5977), , Paulson, C. A. and J. J. Simpson, The temperature difference across the cool skin of the ocean, Journal Geophysical Research, 86(C11), , Price, J. F., C. N. K. Mooers and J. C. Van Leer, Observation and simulation of storminduced mixed-layer deepening, Journal of Physical Oceanography, 8, , Price, J. F., R. A. Weller and R. Pinkel, Diurnal Cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing, Journal of Geophysical Research, 91, ,

18 Rice, J. P., S. C. Bender, W. H. Atkins and F. J. Lovas, Deployment test of the NIST EOS thermal-infrared transfer radiometer, International Journal of Remote Sensing, 24(2), , Schluessel, P., W. J. Emery, H. Grassl and T. Mammen, On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature, Journal of Geophysical Research, 95(C8), , Shinoda, T. and H. Hendon, Mixed layer modeling of intraseasonal variability in the tropical western Pacific and Indian oceans, Journal of Climate, 11, , Shukla, J., Predictability in the midst of chaos: A scientific basis for climate forecasting, Science, 282(5389), , Soloviev, A. and R. B. Lukas, Observations of large diurnal warming events in the nearsurface layer of the western equatorial Pacific warm pool, Deep Sea Research I, 44(6), , Stuart-Menteth, A. C., I. S. Robinson and C. J. Donlon, Sensitivity of the diurnal warm layer to meteorological fluctuations. Part 2: A new parameterisation for diurnal warming, Journal of Atmospheric and Ocean Science, 10(3), , Sverdrup, H. U., M. W. Johnson and R. H. Fleming, The Oceans: Their Physics, Chemistry, and General Biology, Prentice-Hall, Englewood Cliff, NJ, Ward, B. and P. J. Minnett, An autonomous profiler for near surface temperature measurements, in Gas Transfer at Water Surfaces, edited by M. A. Donelan, W. M. Drennan, E. S. Saltzmann and R. Wanninkhof, pp , American Geophysical Union Monograph, Webster, P. J., C. A. Clayson and J. A. Curry, Clouds, radiation, and the diurnal cycle of sea surface temperature in the tropical western Pacific, Journal of Climate, 9, , Weller, R. A. and S. P. Anderson, Surface meteorology and air-sea fluxes in the western equatorial Pacific warm pool during the TOGA Coupled Ocean-Atmosphere Response Experiment, Journal of Climate, 9(8), , Wick, G. A., J. J. Bates and D. J. Scott, Satellite and skin-layer effects of the accuracy of sea surface temperature measurements from the GOES satellites, Journal of Atmospheric and Oceanic Technology, 19, , Woods, J. D. and W. Barkmann, The response of the upper ocean to solar heating. I: The mixed layer, Quarterly Journal of the Royal Meteorological Society, 112, 1-27,

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20 6 Figure Captions 20

21 7 Tables Table 1. Individual cruise model performance Vessel Date Mean (K) STD (K) F96 POSH F96 POSH 1 Explorer 07Sep Explorer 28Sep Explorer 08Feb Explorer 22Mar Explorer 28Mar Explorer 05Apr Explorer 22Apr Explorer 03Jun Explorer 07Jun Explorer 05Jul Explorer 07Jul Explorer 12Jul Explorer 02Aug Explorer 09Aug Explorer 25Dec Explorer 13Feb Explorer 21Mar Explorer 30Mar Explorer 27Apr Explorer 16May Explorer 03Aug Explorer 08Aug Explorer 05Oct Explorer 12Oct Explorer 19Oct Explorer 23Oct Explorer 08Feb Explorer 29May Explorer 16Aug Explorer 20Sep Explorer 28Sep Explorer 22Oct Explorer 23May Explorer 28May Explorer 25Jun Explorer 25Jul Explorer 01Aug Explorer 06Aug Explorer 12Aug Explorer 20Aug Ewing 01Sep Ewing 08Sep Ewing 09Sep Ewing 18Sep Ewing 11Oct Ewing 08Nov Ewing 09Nov

22 48 Ewing 10Nov Ewing 11Nov Ewing 13Nov Ewing 14Nov Ewing 15Nov Ewing 17Nov Revelle 30Sep Revelle 01Oct Revelle 02Oct Revelle 09Oct Melville 02Oct Melville 03Oct Melville 05Oct Melville 06Oct Melville 09Oct Melville 10Oct Melville 11Oct Melville 12Oct Melville 13Oct Melville 14Oct Melville 17Oct Melville 18Oct Aurora 11Sep Aurora 13Sep Aurora 14Sep Table 2. Evaluation of model performance for all data. Mean (K) STD (K) Number Obs F POSH

23 8 Figures Figure 1. Diurnal temperature profiles and sigma-t profiles for the R/V Discoverer. The depth of minimum temporal change in heat content is indicated by D (in figures on left side). Figure from Delnore [1972]. Figure 2. Same as Figure 1 but for the R/V Oceanographer. Figure from Delnore [1972]. Figure 3. Vertical temperature profiles in near-surface layer of the ocean in the TOGA COARE domain obtained by free-rising profiler at different wind speeds in the afternoon. From Soloviev and Lukas [1997]. 23

24 Figure 4. Measurements of temperature profiles in the ocean mixed layer (A) 13 January 1993 and (B) 4 February The levels where the skin, true bulk, buoy bulk, and ship bulk SST values are commonly measured are indicated schematically in the diagram. From Soloviev and Lukas [1997]. Figure 5. Semi-log plot of the diurnal temperature range (ΔT) versus depth, March Prepared from hourly averages of the thermistor data. From Halpern and Reed [1976]. Figure 6. SkinDeEP measurements of the upper ocean diurnal thermocline on 10 October The x-axis is local time and each vertical line represents one profile taken as the profiler ascends to the surface. 24

25 Figure 7. Diurnal amplitudes averaged over all 72 days with warming for M-AERI observed sub-skin diurnal warming and two diurnal models. (A) Diurnal Amplitudes as a function of LMT. (B) Diurnal amplitudes as a function of wind speed. (C) Diurnal amplitudes as a function of insolation. 25

26 Figure 8. 3-band and 9-band absorption models. Figure 9. SkinDeEP profiles of the diurnal thermocline. The color of the lines indicates the observed wind speed at the time of the profile. (A) SkinDeEP profiles from 4-11 October (B) Smoothed SkinDeEP profiles from 7-10 October for insolation between Wm -2. (C) The profiles from panel (B) but with the depth normalized by the warm layer depth and normalized heat content. 26

27 Figure 10. Diurnal warming profiles within POSH. Figure 11. Testing dissipation in F96. Top panel: no dissipation in heat, increasing dissipation in wind energy. As the dissipation of mixing energy increases, the warming increases. Bottom panel: no dissipation in wind energy, increasing dissipation of heat in the warm layer, as dissipation increases the warming decreases. 27

28 Figure 12. Sensitivity study of the F96 (panels A and B) and POSH (panels C and D) modeled diurnal warming. Each simulation was performed with a realistically shaped 12- hour day length insolation and constant wind speed. Figure 13. Simulated warming from the F96 (panels A and B) and POSH (panels C and D) models as a function of time of day. Panels A and C were evaluated with wind speed equal to 1.0 ms -1, variable insolation and length of day. Panels B and D were evaluated with daily average insolation equal to 320 Wm -2, variable wind speed and length of day. 28

29 Figure 14. Two local diurnal peaks in a single day. Figure 15. Variable cloud cover and two local diurnal peaks. Figure 16. Late afternoon increase in wind speed. 29

30 Figure 17. This day had an abrupt increase in wind speed. Figure 18. Sharp increase in wind speed. Figure 19. Early peak in warming. 30