Volume 119, Issue 7 p. 4101-4123
Research Article
Free Access

Modeled diurnally varying sea surface temperatures and their influence on surface heat fluxes

Rachel R. Weihs

Corresponding Author

Rachel R. Weihs

Department of Earth, Ocean, and Atmospheric Science, Center for Ocean-Atmospheric Prediction Studies, Florida State University, Tallahassee, Florida, USA

Correspondence to: R. R. Weihs, [email protected]Search for more papers by this author
Mark. A. Bourassa

Mark. A. Bourassa

Department of Earth, Ocean, and Atmospheric Science, Center for Ocean-Atmospheric Prediction Studies, Florida State University, Tallahassee, Florida, USA

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First published: 17 May 2014
Citations: 18

Abstract

A diurnal warming model is used to create a new data set of global, diurnally varying sea surface temperatures (dSSTs) and surface turbulent heat fluxes over a 5 year period. The magnitude of diurnal warming is primarily a function of low wind speed and net heat flux. Differences between each of the surface turbulent fluxes with and without a diurnally varying SST are examined on hourly, daily, and seasonal time scales. Over a 2 month period, maximum averaged diurnal warming is as large as 0.3°C, and latent heat flux is underestimated by as much as 8 W/m2 in the Indian Ocean. They also exceed roughly 0.7°C and 10 W/m2, respectively, up to 25% of the total daytime in the Atlantic. A best-case approach validation shows the model overestimates peak warming and underestimates the duration of the cycle, though the average error is quite small. The model is tested under a variety of wind speed, solar radiation, and precipitation conditions to examine the impact of potential biases or error in the input data. To test the impact of a positive bias in the wind speeds, diurnal warming magnitudes are recomputed with an adjusted wind under near-neutral conditions. Compared to the original data, diurnal warming can increase by as much as 1.5°C on an hourly scale but generally is <0.06°C. Although precipitation effects on dSSTs are small compared to winds and radiation, the model configuration wrongly causes diurnal warming to increase by precipitation, contrary to the underlying model physics.

Key Points

  • Diurnal warming is important to seasonal sea surface temperature variability
  • Surface heat fluxes are underestimated without diurnal variability of SSTs
  • Modeled diurnal cycles are sensitive to wind, heat flux, and precipitation

1 Introduction

Sea surface temperature is one of the primary regulatory factors in driving variations of air-sea interaction on a multitude of temporal and spatial scales. Therefore, sea surface temperatures (SSTs) are vital to applications such as climate monitoring, weather forecasting, nautical operations, biological research, and other areas that depend on understanding heat/energy, mass, and momentum exchange between the ocean and the atmosphere [Kawai and Wada, 2007]. As technology becomes more sophisticated and uncertainties in measurements from these technological resources become smaller, more emphasis is concentrated on understanding the spatial and temporal scales that are important for these applications. Thus, the scientific community has begun to acknowledge that the variability of SSTs on a subdaily scale and its role in the heat budget are becoming increasingly important for these applications.

The diurnal variability of SSTs is described as heating in the upper ocean in which under calm, clear conditions, the net energy absorbed in the upper layers of the ocean causes temperatures to change near the surface. Neglecting horizontal advective effects, if surface momentum fluxes are small and the total energy flux into the ocean is positive, the induced stratification from surface heating reduces the depth of the turbulent boundary layer [Bernie et al., 2007]. Without sufficient turbulence to disperse the heat (and excluding removal through advection and diffusion), the majority of the energy resides within a small layer of the upper ocean, called the diurnal warm layer, in which there is a measurable difference between the sea surface temperature at the boundary of the sea surface and the temperature at a depth of meters or even tenths of meters below. Studies performed with in situ or remotely sensed observations have shown that diurnal heating of the sea surface, or diurnal warming, can be as large as 3 K in the tropical Pacific [Fairall et al., 1996b; Stramma et al., 1986; Soloviev and Lukas, 1997] or as large as 5 and 6 K in the Mediterranean Sea and North Sea [Merchant et al., 2008; Gentemann et al., 2008]. Conversely, the diurnal warm layer can dissipate over time by a number of processes including entrainment into the mixed layer by wind-induced surface stress or vertical shear, reduction of absorbed solar energy, or turbulence from nighttime convection. Overnight, diurnal warm layers typically mix out completely and the surface temperature reaches a nighttime minimum, usually closest to the mixed-layer temperature for the next day [Gentemann et al., 2009].

Modeling the diurnal variability of SSTs has become an important task in producing climate quality global SST data. For instance, comparisons between satellite-retrieved SSTs and in situ measurements at depths of 1 m can be problematic under clear sky and low wind conditions; in the presence of diurnal warming, the temperature profile may not be vertically homogeneous and the “sea surface temperature” observations near the surface, where satellites measure temperature, can be different from measurements at 1 m depth [e.g., Kawai and Wada, 2007; Fairall et al., 1996b; Price et al., 1986]. Hence, calibration techniques of satellite-retrieved SST using buoy measurements as truth will lead to biases in the retrievals if diurnal warming is not accounted for [Embury et al., 2012; Donlon et al., 2002]. Models that can also reproduce the upper ocean vertical structure with diurnal variability are valuable for homogenization of SST products at various depths. Additionally, Kawai and Wada [2007] and Clayson and Curry [1996] concluded that high-frequency SST variations need to be considered to improve surface flux accuracy on daily-mean surface heat fluxes. Surface heat fluxes that include diurnal variability of SSTs can be used to better estimate the upper ocean energy budget. Diurnal warming has been shown to influence climate-scale variability as large diurnal variations of SST are found during the suppressed phase of the Madden-Julian Oscillation, or MJO [Kawai and Wada, 2007]. Theories of diurnal warming's influence on MJO go as far as to suggest that it play a role in the duration of the suppressed convection phase and the onset of active phases [Slingo et al., 2003]. Woolnough et al. [2007] compared coupled model simulations with and without a diurnally varying SST and concluded that the diurnal varying SST model run had better predictive skill for phases of MJO over the western Pacific and Indian oceans. Links to atmospheric modifications, such as temperature retrievals from Microwave Sounding Units, have also been shown to be influenced by diurnal variability throughout the troposphere [e.g., Kennedy et al., 2007].

The goal of this research is to explore diurnal variability through the use of a physically based diurnal warming and surface turbulent heat flux model to develop a high-resolution, diurnally varying SST field in the hopes that it will improve understanding of diurnal variability of SSTs and surface heat fluxes on diurnal and seasonal time scales. A data set consisting of diurnal temperature change in SST and surface heat fluxes from 2000 to 2004 is produced using reanalysis data as input. Diurnal warming and its influence on surface heat fluxes are then analyzed over daily and semiseasonal time scales to identify characteristic features of diurnally variability, including the amount of diurnal temperature change, spatial distribution, and spatial and temporal frequency. In addition, a short sensitivity study of the model to particular inputs as well as model assessment to satellite SST data are performed. A summary of the diurnal warming model and explanations of modifications and corrections are presented in section 2. Key characteristics of modeled diurnal warming on daily and semiseasonal scales including the semiseasonal average magnitudes on the order of a few degrees and the associated surface flux impacts are described in section 3. A preliminary validation of diurnal warming to satellite data showing the model performance is given in section 4. Model sensitivity studies of the dependence on winds, solar radiation, and precipitation that show stability and low wind speeds are important while results on precipitation are inconsistent are explained in section 5. A summary and discussion are given in section 6.

2 Diurnal Warming Model

2.1 Description of Diurnal Warming Model

In this study, diurnal warming is simulated using a modified version of a physical-empirical hybrid, one-dimensional ocean heating model called the Profiles of Oceanic Surface Heating Model (abbreviated as POSH) [Gentemann et al., 2009]. The POSH model is primarily derived from Fairall et al.'s [1996a] warm layer/cool-skin model in the Tropical Ocean-Global Atmosphere (TOGA) Coupled Ocean-Atmospheric Response Experiment (COARE) bulk flux algorithm (v2.5b) [Fairall et al., 1996b] (note that the COARE flux algorithm is now up to version 3, but has not been used in the POSH model). The TOGA COARE bulk flux algorithm computes diurnal warming from local bulk atmospheric variables (air temperature, specific humidity of the air, wind speed, and surface pressure) as well as ocean temperature made at a depth z and surface incident radiative fluxes to calculate the diurnal variability of SSTs using physics of the mixed layer.

The ocean temperature at depth z has been referred to by many names, such as mixed-layer temperature, bulk temperature, or even sea surface temperature when observed by buoys, drifters, etc. It is important to distinguish the reference temperature being discussed because of the variable vertical structure of the upper ocean, especially in the presence of diurnal warming. In order to avoid confusion, we will use the nomenclature consistent with Donlon et al. [2007] in which the sea surface temperature computed in the model is referred to as skin temperature (SSTskin) and the ocean temperature at depth z is referred to as SSTdepth. Note that the depth of SSTdepth can be specified in the model, depending on the particular type of input data. For this study, the SSTdepth will be set to a depth of 19 m; this is an estimate of the depth at which no diurnal variability influences the temperature (C. Gentemann, personal communication, 2011). Therefore, the more appropriate term for the ocean temperature input in this study is SSTfnd or foundation sea surface temperature. More specific terminology is provided in section 2.1.1.

POSH was created to improve the physical parameterizations of the COARE bulk flux model (herein referred to as COARE2.5) in regards to the diurnal variability of SSTs using, in part, ship-based observations in the Pacific [see Gentemann et al., 2009]. In addition, POSH was chosen for this study on the basis of physical, albeit bulk parameterizations (as opposed to empirical models with little or no representation of the underlying physical processes), having “turbulence closure-like vertical structure,” and remaining less computationally expensive than other full-ocean physics models [Gentemann et al., 2009]. Though Gentemann et al. [2009] have provided a model evaluation based on data from research vessel cruises, to our knowledge, we have not seen a study that examines the capabilities of POSH on a global scale under a wide variety of atmospheric and oceanic conditions.

2.1.1 POSH Method for Computing Diurnal Heating

Like COARE2.5, POSH computes the diurnal variability of SSTs from bulk atmospheric and ocean variables and radiative fluxes at the surface by means of accumulated heat and momentum. The model is designed to compute the diurnal warming magnitude, dSST, which is defined as the hourly difference between SSTdepth and the warmest temperature within the diurnal warm layer in the upper few meters of the ocean. Typically, the warmest temperature in the diurnal warm layer is at a depth less than a few millimeters [Fairall et al., 1996a], as the skin temperature is modified by a sublayer where, on the molecular level, evaporation and diffusion produce heat loss. This is known as the cool-skin layer [Kawai and Wada, 2007; Fairall et al., 1996a]. Thus, urn:x-wiley:21699275:media:jgrc20704:jgrc20704-math-0001 is described as
urn:x-wiley:21699275:media:jgrc20704:jgrc20704-math-0002(1)
[Gentemann et al., 2009; Donlon et al., 2007; Fairall et al., 1996a]. Note that the cool-skin term is kept separated from the diurnal warm layer; this is to remain consistent with the POSH model. Measurements of diurnal warming are usually the combined effect of warming and the cool-skin correction. If the wind stress is minimal enough to reduce mechanical mixing and net heating in the ocean becomes positive as solar energy is absorbed, the upper ocean becomes stratified. Mathematically, this occurs by accumulating heat until it reaches a positive value (in the ocean). If the heating is positive, then a diurnal warm layer can be computed. A full model description is given in Gentemann et al. [2009].

When a diurnal warm layer is present, the diurnal warming magnitude is added to the foundation temperature to create a subskin temperature to which the cool-skin adjustment from COARE2.5 is subtracted. The surface heat fluxes are calculated with the cool-skin corrected skin temperature. If no diurnal warming has occurred, the skin temperature is equal to the foundation sea surface temperature.

2.1.2 Global Reanalysis Data and Model Modifications

POSH originally computed diurnal warming magnitudes on a local scale, requiring input of bulk variables typically taken from buoy and research vessel measurements [see Gentemann et al., 2009]. To study diurnal heating of the ocean globally, the model is reconfigured to process global input data. First, the model requires a continuous time series of hourly data spanning a full 24 h period to integrate the energy and forcing correctly (C. W. Fairall, personal communication, 1996). Reanalysis data provide continuous, gridded global data spanning decades, which proves to be an optimal choice for POSH. Not all reanalyzes are suitable, however; in a study by Bellenger and Duvel [2009], POSH's parent model, COARE2.5, was used to calculate diurnal warming on a global scale using ECMWF ERA-40 data, which they interpolated from every 6 h to an hourly time step. The disadvantage to this approach is that time interpolation of data has the potential to alias the high-frequency variability that is important to the diurnal cycle. Alternatively, NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA) product (available at NASA's Global Modeling and Assimilation Office (GMAO) and GES DISC) provides hourly data of all the necessary components (wind vector components, air temperature, and specific humidity at the standard 10 m height, air pressure, precipitation rate, surface incident shortwave flux (with clouds), and surface absorbed longwave flux) needed to model diurnal warming using POSH.

Second, the SSTdepth temperature needs to be representative of a foundation temperature [Donlon et al., 2007] as previously mentioned in order to quantify the total warming magnitude in the column. Though qualitatively, a foundation temperature is easily definable, in practice there is no defined depth to which this temperature is found. In certain applications, foundation sea surface temperatures can be approximated as a predawn or nighttime minimum temperature [Kawai and Wada, 2007]. For this study, we use the Reynolds AVHRR-only Daily OI Sea Surface Temperature (SST) [Reynolds et al., 2007] data set as a proxy for foundation temperature. The Reynolds daily OI SST product uses satellite and in situ products to create a blended daily averaged sea surface temperature; the daily averaging reduces the effect of diurnal variability of the SST [Reynolds et al., 2007], though there may be a residual diurnal variability bias. Additionally, the satellite data used to create the daily OI SST are bias adjusted to in situ data over a 7 day period, further “reducing the diurnal variability” according to Reynolds et al. [2007] but may be more accurately described as aliasing the true diurnal variability into the weekly scale. Presently, there are other sea surface temperature data sets explicitly representing a foundation temperature available as part of the Group for High Resolution Sea Surface Temperature (GHRSST) project. The choice of 19 m for the depth is somewhat subjective; however, observations of the upper ocean vertical structure as well as models of the diurnal warm layer depth show that under strong diurnal warming, the diurnal warm layer depth is typically <10 m [Gentemann et al., 2009; Bellenger and Duvel, 2009; Shinoda, 2005].

Further modifications are made to the POSH model when processing global data. In short, calculations for solar zenith angle, solar insolation, and hour of dawn are updated (see Appendix Appendix B). Atmospheric variables made at a 10 m height are reprogrammed to be ignored in the height adjustment computations since they are made at the standard height. Grid cells which have a nonzero ice concentration value from the Reynolds OI daily averaged ice data set [Reynolds et al., 2007] are excluded from the model and are set to missing values. Finally, model changes are made to compensate for the very small percentage of data (<<0.001%) that exhibit unrealistically large diurnal warming magnitudes (>10°C) not seen in any previous study. The instability of the iteration computations in the model that cause these unrealistically large diurnal warming magnitudes are a common problem with bulk flux models in extreme conditions where winds are nearly calm and large air-sea stability exists (note, improvements made in version 3 of the COARE algorithm may help resolve this issue but the version 3 has not been tested using POSH). To eliminate the occurrence of unreasonably large dSSTs, the COARE2.5 flux model is replaced with the look-up table flux model from Bourassa [2006] (herein referred to as BVW06) and a threshold restriction is placed on the wind stress when its value is <10−4 N/m2. Both the new flux model and the masking threshold individually improve POSH performance slightly by decreasing the number of erroneous results, but do not eliminate them. Furthermore, as shown in Figure A1 winter polar latitudes have a higher frequency of erroneous diurnal warming (in this case, diurnal warming magnitudes >10°C), suggesting that the presence of ice in the ocean and atmospheric data sets is not fully coincident (or removed, in this case) and requires further attention. We continue with the assumption that ice is not well resolved between the input data, so the output is filtered to remove the small number of occurrences where dSSTs are larger than 10°C. More details of the changes are provided in Appendix Appendix A.

2.1.3 Implementation

The systematic approach to generating a diurnally varying sea surface temperature data set is as follows: for a given day, a 72 h period of input data from the current, previous, and following days is ingested into the model. For each grid point, initialization and start time are determined by the time of local dawn in GMT. Hour of dawn is calculated using the algorithm from Nautical Almanac Office [1989] and rounded down to the nearest hour. Another hour is subtracted from the start time to allow the model one time step to initialize. Note that the model is running in local time and all grid points have different starting times depending on latitude and season. The Reynolds SST is used as a foundation sea surface temperature and set to a depth of 19 m and all other data are initialized. The model then processes the hourly data for a local 24 h period for a complete diurnal cycle.

Following the completion of a 24 h cycle, the accumulated heat and momentum parameters are reset; this is analogous to the erosion of the diurnal warm layer overnight via convection. For polar latitudes that do not experience a time of dawn (days with continuous sunlight or darkness), the nearest latitude's dawn value within the same longitude band is used as the reset time. This is a best guess estimate at which diurnal warming in the arctic regions would be at a minimum, though in reality, diurnal warming may never “reset” with constant solar flux. Cases in which diurnal warming does not “reset” at the end of the 24 h cycle are rare within the data set and are usually <0.1°C.

Each model run produces an hourly diurnal warming magnitude (dSST) and skin temperature (SSTskin) as well as sensible and latent heat fluxes from the BVW06 model with and without diurnal heating at 0.25° resolution. Although the dSST does not reflect a cool-skin offset, all fluxes are computed with a cool-skin adjustment, even without a diurnal heating effect. This is justified because the cool-skin effect is almost always present during both day and night [e.g., Gentemann et al., 2008, Stuart-Menteth et al. 2003], and in turn, reduces the potential for overestimation of the total flux differential between SSTs with and without diurnal heating [Bellenger and Duvel, 2009]. Finally, the current 72 h data file is concatenated with the 72 h data from the previous and following days, with overlapping times replaced by data from the previous day. They are then separated again into individual 24 h GMT data files.

2.2 Turbulent Surface Heat Flux Differences

Typical bulk formulae are used in this study to compute sensible and latent heat fluxes with and without a diurnally varying SST. Latent heat flux is given as
urn:x-wiley:21699275:media:jgrc20704:jgrc20704-math-0003(2)
where ρ is the density of air, LE is the latent heat of vaporization, CE is the Stanton number, U10 is the wind speed at the standard height of 10 m, and qs and qa are the specific humidity of the sea surface (reduced to 98% for saturation value over salt water) and air, respectively. In this study, positive energy fluxes translate to fluxes out of the ocean.
To quantify the impact of diurnal heating on surface turbulent fluxes at any given time, the difference between the heat flux with a diurnally varying SST and that of SST equivalent to a constant foundation temperature was computed at each time step for the entire data set. So:
urn:x-wiley:21699275:media:jgrc20704:jgrc20704-math-0004(3)

Thus, latent heat flux difference is nonlinearly dependent on the wind speed, latent heat transfer coefficients (dependent on SST), and the air-sea humidity difference. Similarly, sensible heat flux is dependent on the wind speed, sensible heat transfer coefficients, and air-sea temperature difference.

2.2.1 Sensitivity of the Components of the Latent Heat Fluxes With Respect to Diurnal Warming

The impact of diurnal warming on latent heat fluxes is determined primarily by the humidity difference between the air and ocean and mechanical mixing due to winds. In order to produce diurnal warming, wind speeds must be relatively small; however, this will also act to reduce latent heat fluxes. Instead, at certain low wind speed ranges, the humidity difference, or more generally, the air-sea stability must play a bigger role. Changes in humidity can be directly linked to temperature via the Clausius-Clapeyron equation (specifically Tetens' formula), which is a function of the interfacial temperature (and pressure):
urn:x-wiley:21699275:media:jgrc20704:jgrc20704-math-0005(4)
where e0 is 0.611 kPa, T0 is 273 K, Rv is the gas constant for water vapor, and Lv is the latent heat of vaporization. Linear changes in temperature produce nonlinear increases in vapor pressure. To show the general expectation to changes of latent heat fluxes with and without diurnal warming, the BVW06 model is forced with low wind speeds ranging from 0 to 10 m/s at every 0.1 m/s interval and sea surface temperatures ranging from 0 to 30°C at every 0.1°C interval, while the air temperature is kept at a constant 15°C. The specific humidity for this example is computed based on the saturation vapor pressure of water and a surface pressure of 1020 hPa. The latent heat flux difference is computed as given in equation 3. The turbulent coefficients are computed separately where urn:x-wiley:21699275:media:jgrc20704:jgrc20704-math-0006 is determined by the assigned sea surface temperature and urn:x-wiley:21699275:media:jgrc20704:jgrc20704-math-0007 is forced with the assigned sea surface temperature plus an additional 1°C for diurnal warming. Similarly, the specific humidity, urn:x-wiley:21699275:media:jgrc20704:jgrc20704-math-0008, is computed with the additional diurnal warming of 1°C. From this sensitivity study, we observe several important features; the change in latent heat flux (shown in Figure 1) is always positive when incorporating diurnal warming, but the rate at which it increases is heavily dependent on the air-sea humidity difference and wind speed. Second, the fluxes near neutral stability are affected by the ability of the flux model to resolve the discontinuity between the transfer coefficients computed between nearly positive and nearly negative air-sea temperature differences [Liu et al., 1979]. A gustiness parameter used in COARE2.5 is used but is not 100% effective in creating a smooth transition between stable and unstable regimes. And finally, below winds of roughly 1 m/s, latent heat fluxes become more dependent on humidity gradients and very low wind speeds (see section 5.1). The sensible heat flux differences (Figure 1, top) behave in a similar fashion, though winds and temperature are more linearly related. Note that certain atmospheric feedbacks are not included in this model; likely the fluxes would be modified by the gustiness parameter (which is included in POSH), free convection, modification of the air temperature, etc. For the remainder of the paper, all latent (sensible) heat flux differences will be reported as the value of the latent (sensible) heat flux with a diurnally varying sea surface temperature subtracted by that which is computed with a constant daily foundation SST.
Details are in the caption following the image

(top) Sensible heat flux differences and (bottom) latent heat flux differences as a function of wind speed and air-sea temperature difference. The latent heat flux differences are computed via equation 3, and the transfer coefficients are computed from the BVW model [Bourassa, 2006]. Air temperature is 15°C, 10 m specific humidity is 0.008 kg/kg. Negative values are regimes in which air is warmer than the ocean and positive fluxes are out of the ocean.

3 Features of POSH Modeled Diurnal Warming

3.1 POSH Model Daily Features

Diurnal warming is a sun-synchronous feature of the ocean (Figure 2), but the spatial and temporal distributions vary greatly from location to location, depending on local conditions. Though it is not uncommon to observe large diurnal warming magnitudes in the high-latitude oceans using satellite data, the majority of concentrated areas with larger magnitudes of warming around 3°C primarily reside within the tropics and subtropics in large clusters or streaks. Moreover, patterns of diurnal warming reflect the local current meteorological state; large midlatitude cyclones and other high wind or largely convective systems that inhibit heating are evident, for example, off the west coast of Japan in Figure 2a.

Details are in the caption following the image

Evolution of the diurnal heating amplitude (dSST °C) over the course of the day. Each box is a snapshot of dSST on 6 April 2002 at (a) 00:30Z, (b) 07:30Z, (c) 15:30Z, and (d) 23:30Z.

A prominent feature present in the data set is the occurrence of diurnal warming “streaks” found in the tropics and midlatitudes. Figure 3 shows two examples in which diurnal warming magnitude equal to or larger than 0.5°C extends along a thin, wide swath across thousands of kilometers. These streaks have also been noted in other studies [e.g., Stramma et al., 1986; Bellenger and Duvel, 2009]. In the presence of daylight, these streaks of diurnal warming magnitudes are highly correlated with the wind field. QuikSCAT swath wind speed data from Remote Sensing Systems (Figure 3, middle row) are used for visual wind speed verification. Data from both cases of diurnal warming show there is good agreement with low wind speeds and the large amplitude of warming. For these two cases, warming coincides with low winds in the center of the Azores High in the Atlantic Ocean (Figure 3, left column) or with low wind speeds on the outskirts of a low-pressure system in the Pacific Ocean (Figure 3, right column). For the Pacific Ocean warming event, the maximum diurnal warming magnitude is roughly 2.88°C.

Details are in the caption following the image

Two cases of large diurnal warming “streaks” on 10 July 2002 at (left column) 16Z and (right column) 23Z. The top row contains diurnal warming magnitudes (shaded), surface pressure (solid lines), and wind speed (dashed lines). The middle row contains composite QuikScat wind speeds (ascending and descending passes) on 10 July 2002. The bottom row contains the latent heat flux difference (shaded), surface pressure (solid lines), and wind speed (dashed lines) for the same time.

The influence of diurnal warming on latent and sensible heat fluxes on a daily scale is also examined. For the Pacific Ocean warming event, instantaneous differences in the latent heat flux in association with the maximum dSST are as large as 51.72 W/m2. Similar values of maximum warming and flux perturbations have been observed in actual data taken in the tropical Pacific where diurnal warming is present [Fairall et al., 1996b]. While these substantial differences between temperatures and fluxes are quite significant on their own, it may be argued the large, short-lived diurnal heating events are too infrequent to impact the fluxes even on daily scales. However, moderate warming, say from 0.5°C to 1.5°C, commonly coincides with fluxes computed with diurnal warming that are equal to or larger by 10 W/m2 for more than half of the daylight hours in the data set. For example, warming of 0.67°C near the edges of the warming streak in the Atlantic shown in Figure 3 persisted for more than two thirds of the daylight time and had average latent heat flux differences in excess of 15 W/m2. Similarly, Webster et al. [1996] found changes of 18.7 W/m2 in the latent heat flux during the TOGA COARE IOP in association with a 1°C SST change. The modeled global-averaged latent heat flux change in which dSSTs >1°C within the 5 year period of this study is 18.57 W/m2.

3.2 Diurnal Warming on a Semiseasonal Scale

To quantify diurnal warming of the ocean on a seasonal time scale, bimonthly composite fields of diurnal warming magnitudes are created by taking the mean of the averaged dSST in a 2 month period over the 5 total years. Each bimonthly period of the year, from January and February until November and December, is analyzed to identify areas of persistent dSSTs on roughly seasonal scales (Figure 4). A bimonthly time scale is chosen as a good approximation of seasonal features of diurnal warming, yet it is thought to be small enough to allow some intraseasonal variability. Since the global distribution of diurnal warming is significantly skewed toward zero, the averaged composites will pinpoint only areas where the amplitude of warming is consistent from day to day and persistent throughout the day.

Details are in the caption following the image

Two month averaged diurnal warming magnitude (dSST) composites for all six bimonthly periods of the year. The composites contain the averages computed for all observations occurring in the 2 month period over all 5 years from 2000 to 2004.

The strong seasonality of diurnal warming has been well documented in various diurnal SST observational and modeling studies [e.g., Kawai and Wada, 2007; Bellenger and Duvel, 2009; Clayson and Weitlich, 2007] and is clearly evident in POSH-based estimates. Seemingly broad, ocean-basin-wide bands of diurnal warming migrate toward the north and south in accordance with the seasonal cycle of the sun. Conversely, the extent of diurnal warming in polar latitudes is severely limited because of sea ice extent (by design) and high winds associated with storm tracks.

The spatial distribution of seasonally persistent diurnal warming is well detailed by Clayson and Weitlich [2007], but is summarized here and shown in Figure 4. Regions of diurnal warming “hotspots” are typically collocated with areas of seasonal climatologically low wind regimes. For example, dSST is favored in the eastern Pacific during the early months of the year because of the slow trade winds, despite convection along the Intertropical Convergence Zone (ITCZ). Additionally, the Pacific waters south of Mexico's Sierra Madre mountain range experience large diurnal warming throughout the first half of the year because the high mountainous terrain obstructs northeasterly winds from the Gulf of Mexico. Frequent year-round diurnal warming is also found in the convergent wind zone off the West African coast, as well as Indian Ocean and the extreme western Pacific in association with the phases of the Asian monsoon. In addition to those features noted by Clayson and Weitlich [2007], large diurnal warming is also evident in the Mediterranean Sea, Red Sea, and Persian Gulf during boreal summer, and in the Timor Sea during fall.

Given the asymmetrical distribution of dSSTs, it is expected that the average magnitude of warming over a 2 month period is much less than that over shorter time scales. However, during July and August, >30% of the North Atlantic and North Pacific ocean basins exhibits an average diurnal warming amplitude over one-tenth of a degree, which surpasses the accuracy target of 0.1°C in sea surface temperatures measurements on climate time scales [Bradley et al., 2006]. Consequently, composite maps of surface turbulent heat flux differences (Figure 5) show that latent and sensible heat fluxes are underestimated by a minimum of 4 and 0.5 W/m2, respectively, where seasonal warming is greater than one-tenth of a degree. At the higher end, the surface flux deficits can be as large as 8 W/m2 in the equatorial Pacific and northern Indian oceans. In addition, several studies [Kawai and Wada, 2007; Bellenger and Duvel, 2009] found that the latent heat flux in particular accounts for only two-thirds of the total heat budget affected by diurnal warming; longwave radiation also increases because of increased energy emittance, thus the potential for the total heat budget error to exceed the 10 W/m2 accuracy threshold set forth in the TOGA-COARE project [Fairall et al., 1996b]. According to Kawai and Wada [2007], increased heat fluxes into the atmosphere of this magnitude are nonnegligible and could lead to destabilization of the lower atmosphere. Their conclusion also supports the theory of diurnal warming and its influences on local diurnal convection in the tropics [Clayson and Weitlich, 2007].

Details are in the caption following the image

Composite bimonthly averaged latent heat flux differences for each 2 month period in the year. Differences are computed subtracting the flux computed with a foundation SST from that with a diurnally varying SST at each time step and averaging over all time steps in a 2 month period.

3.3 Comparison of dSST in Tropics and Midlatitudes

Many studies on diurnal warming focus on the tropical oceans between 30°N and 30°S, where buoy systems, such as TOGA-TAO, and research vessel missions provide data for comparison and verification [e.g., Soloviev and Lukas, 1997; Gentemann et al., 2009; Price et al., 1986; Bellenger and Duvel, 2009; Shinoda, 2005; Webster et al., 1996; Clayson and Weitlich, 2007; Gentemann et al., 2004; Shinoda and Hendon, 1998]. It is also logical to limit diurnal warming studies to the tropics since the conditions within the tropics create a favorable environment for diurnal warming. However, satellite observations and modeled data [e.g., Merchant et al., 2008; Gentemann et al., 2008], including POSH, have demonstrated that diurnal warming is not limited to the tropics; midlatitudes can experience a similar magnitude of warming, depending on the season. If relying only on the average diurnal warming computed in section 3.2 as a means of identifying regions highly impacted by the changes in sea surface temperature and its associated heat fluxes, the mid and higher latitudes may be underestimated; here, multiple-day warming is often interrupted by synoptic-scale weather events (i.e., a midlatitude storm passes through the region). The average of a process that is highly variable in time may not truly convey the occurrences of large diurnal warming events or its impact on the climate. An alternative method used to understand the impact of diurnal warming, rather than averaging, is analyzing the total consecutive time in which diurnal warming exceeds a threshold as a percentage of the total time period. Bellenger and Duvel [2009] studied the persistence of diurnal warming in the tropics from 30°N to 30°S using COARE2.5 and ERA-40 reanalysis. They found that diurnal warming magnitudes in the tropics >0.67°C can occur between 10% and 50% of the day for an entire 3 month season. They also showed that these large diurnal warming events could reoccur for >5 consecutive days. A similar analysis may be problematic for the midlatitudes for reasons previously mentioned. Instead of a comparison of consecutive days with diurnal warming, composite two-monthly maps are constructed for the total time (specifically, daylight hours) that diurnal warming magnitudes exceed a threshold within a 2 month period for all latitudes. Figure 6 shows the percentage of daylight hours when diurnal warming is >0.67°C for the northern midlatitudes and tropics (top) between 60°N and 60°S during July and August of 2002. The 0.67°C threshold is motivated by Bellenger and Duvel [2009] as it is approximately equal to their average dSST plus one standard deviation using POSH's parent model, COARE bulk flux algorithm in the hopes that similar features can be identified given the similar physics in the two models.

Details are in the caption following the image

(top) Percentage of daylight hours in which dSSTs exceed 0.67°C for the entire bimonthly period of July and August of 2002 for the northern midlatitudes and tropics. (bottom) Percentage of daylight hours in which latent heat flux differences are greater 10 W/m2 for the entire bimonthly period of July and August of 2002 for the northern midlatitudes and tropics.

As compared to the results in Bellenger and Duvel [2009], the regional areas marked by higher occurrence rates in both studies are strikingly similar between 0° and 30° latitude. The magnitudes of occurrence are not meant to be directly compared, as they are examining different time scales of persistence (percentage of a day versus percentage of the daylight hours for the entire time period), but nonetheless confirm the persistence of diurnal warming in these areas. With the persistence of diurnal warming in the tropics used as a baseline, we compare it with that in the midlatitudes. The two latitude bands both experience similar time frames (about 10–25% of the time period) in which diurnal warming is larger than 0.67°C. In fact, almost half of the North Atlantic Basin between 30°N and 40°N experiences heating >10% of the time. Keeping in mind that the percentage represents the total number of daylight hours in the entire 2 month period, a 10% timely occurrence means diurnal warming above 0.67°C can exist almost 86 total hours, the equivalent of almost 4 days. Similarly, the percentage of daylight hours in which dSST-induced changes in latent heat fluxes, for example, exceed 10 W/m2 is computed for the same 2 month period (Figure 6, bottom). Once again, the percentage of daylight hours in which latent heat fluxes are underestimated by 10 W/m2 occurs up to 25% of the time in the Atlantic Ocean. For climate applications that are sensitive or dependent upon the transfer of heat and moisture from the ocean to the atmosphere, the latent heat flux deficits of this magnitude cannot be ignored without introducing a systematic bias in the results. This bias is seasonally and regionally dependent, given the global climatology of winds; for instance, results show that during austral summer (not shown), diurnal warming in the Southern Pacific and Southern Indian Ocean is less frequent due to the overall stronger winds found in the midlatitude oceans of the southern hemisphere.

4 Comparison of POSH to Satellite Data

POSH-generated SSTs are compared to a sample set of satellite-retrieved SST data to examine how well POSH can represent the diurnal cycle over the Atlantic Ocean. The EUMETSAT Ocean Sea Ice Satellite Application Facility experimental SST product provided by IFREMER is an hourly SST product based on the Spinning Enhanced Visible and Infrared Imager (SEVIRI) SST data. It is primarily used for the comparison since the satellite's geostationary orbit allows for frequent sampling over the Atlantic and Mediterranean waters on a high-resolution, 5 km, hourly grid with robust cloud flagging [Derrien and Le Gléau, 2005]. Furthermore, the algorithms used to retrieve SST are the same for day and night as to remain consistent for diurnal studies that compare nighttime and daytime differences [Merchant et al., 2008]. Le Borgne et al., [2007] compared SEVIRI SSTs to drifting buoys and found a standard deviation of 0.5°C and a negligible overall bias. For this application, the satellite data will be considered truth, where appropriate, and compared to POSH dSST.

As a first guess estimate of the skill of POSH, a set of sample dates in midJanuary, March, July, and October 2009 are chosen to analyze the model and satellite data. To collocate POSH and SEVIRI SSTs, the satellite data are interpolated to match the 0.25° resolution of the model data by means of a bilinear interpolation method. When analyzing the SST differences between the two products, differences at each time step are not sufficient to determine the quality of the representation of the diurnal cycle in POSH since the differences in SST can also be functions of a nighttime bias between the foundation temperature and the satellite nighttime temperature, and/or time difference of the onset timing of the cycle. Furthermore, the caveats associated with gap filling by the interpolation technique can deteriorate the quality of the comparison, especially when the satellite data are not continuous over time. To establish quality criteria, a spatial coverage density map is used to determine the percent of coverage per 0.25° grid cell. The coverage density is a combined measure of the density (how many satellite grid points lay within the 0.25° cell) and the continuity (how often, in hours, the grid cell is sampled over the day) expressed as a percent. The daily coverage density map for 22 July 2009 (Figure 7, left) shows that SSTs are well sampled for most of the Mediterranean and more sporadic in the tropical and subtropical Atlantic Ocean, with the exception of a large low wind speed feature east of North America.

Details are in the caption following the image

(left) SEVIRI SST coverage percentages for a 0.25° cell on 22 July 2009. (right) Time series of regridded SEVIRI SST (dark blue) and POSH dSST (light blue) for five sample points with coverage >80% with (top plot) a peak dSST value >0.5°C, (middle plot) mean bias of POSH minus SEVIRI differences for all results as a function of hour, and box and whisker plots showing the distribution of the bias for each hour with the median marked by a red line, the edges of the boxes representing 25th and 75th quantiles, and edge of the whisker representing the 5th and 95th percentile of the data. POSH SSTs are adjusted based on the mean foundation temperature minus predawn temperature.

The percent spatial coverage density is used to select grid points that are well-sampled satellite SST data over the day; in this case, a threshold of 80% is used for the domain between 55°W and 40°E and 25°S to 50°N. A large threshold is ideal in order to reduce the chance of a bias from lack of data in space and time. In addition, only grid cells that have a diurnal peak larger than 0.5°C are used to insure that the SST diurnal variability primarily represents more true diurnal variability than artificial variability due to noise in the SST measurement. Each of the ∼3600 sampled points that meet the threshold criteria are then analyzed over each hour (in GMT) to determine the overall diurnal cycle representation in POSH. A mean nighttime bias of −0.43°C (Reynolds minus SEVIRI) is found by averaging the differences between the Reynolds SST product and the SEVIRI predawn temperature for the first 5 h in the day. The bias is surprisingly large for the months of March and July compared to typical SST accuracy thresholds. It is not clear whether the errors are from the Reynolds OI SST or nighttime SEVIRI observations and warrants further investigation. The POSH SSTs are increased by the nighttime bias in order to remove systematic errors in the peak SSTs from POSH and SEVIRI based on nighttime temperatures. Because the bias is seasonally dependent, the errors cannot be completely eliminated. Example time series of POSH and SEVIRI SSTs are given in Figure 7 (right, top plot) and show the characteristic curves of diurnal variability within each product, while the mean error (POSH minus SEVIRI) at each hour is given in the right middle plot. The right bottom plot in Figure 7 shows the distribution of the errors at each hour.

A summary of the bias results for all sample dates as well as those in a particular month are located in Table 1. The mean of the time series shows that POSH on average overestimates the peak of the cycle by roughly 0.12°C but with a standard deviation of 0.81°C. During the month of March, overestimations of the peak dSST are 0.6°C on average and can be almost 2° larger in some extreme cases, while in January and October, biases in the foundation temperature and SST at POSH peak are much smaller. In Gentemann et al. [2009], the solar radiation absorption profile was increased by 20% in order to reduce the difference of the model and the regional ocean profile measurements used in the study. However, the overestimation of the peak during March and July indicates that the increase in solar radiation absorption could be a major source of error. Moreover, it appears that the onset of the warming cycle as well as the decay of warming at the end of the day occur prematurely; POSH dSSTs reach their peak magnitude approximately 3 h earlier than SEVIRI SSTs and conversely remain colder on average after SEVIRI has reached its peak. This is consistent with Zeng and Beljaars [2005] as they reported that the nonequilibrium in their model occurring near or after sunset between the buoyancy flux and stable stratification causes a reduction in the computed diurnal warming. The exception is the POSH dSSTs occurring in March that are too warm throughout peak timing in both POSH and SEVIRI. These results are particularly significant to the durations of diurnal warming presented in section 3.3; because an exceedance threshold is used, an overestimation of the peak magnitude would likely overshadow the impact of an underestimation of the duration of diurnal cycle with a similar diurnal cycle shape. The impact on surface heat fluxes are even more ambiguous as a decrease in POSH diurnal warming magnitudes would decrease the change in heat fluxes, but a longer duration of the cycle would likely increase changes in heat fluxes.

Table 1. Average Biases of POSH-SEVIRI SST During 21–23 January 2009, 21–23 March 2009, 21–23 July 2009, and 21–23 October 2009 With a Foundation Minus Predawn Bias Correctiona
Mean Bias In January March July October All
Foundation-Predawn 0.062 −0.604 −0.53 −0.05 −0.431
Peak magnitude (°C) −0.151 0.599 −0.01 0.144 0.116
Peak time (h) −2.833 −3.97 −3.162 −1.60 −3.047
Whole cycle (°C) −0.141 0.138 −0.047 −0.003 −0.012
SST difference at POSH peak time (°C) −0.131 0.717 0.221 0.113 0.237
SST difference at SEVIRI peak time (°C) −0.355 0.133 −0.180 −0.01 −0.095
Total points 227 658 2152 556 3593
  • a All biases are calculated as POSH data minus SEVIRI data.

Encouragingly, the average difference between all data throughout the diurnal cycle is fairly small (−0.012°C). One possibility is that POSH may correctly estimate the total heat content in the upper ocean correctly and the dissipation coefficients of heat and momentum and other warm layer variables in the POSH model should be further investigated. Another is that the diurnal variability of winds, which is crucial to SST diurnal heating, is misrepresented (i.e., smoothed diurnal wind curve in MERRA) or that overestimations in the heat absorption profiles need be reassessed.

5 POSH Model Sensitivity

In the previous sections, we have demonstrated the ability of POSH to model diurnal warming under a wide variety of physically realistic atmospheric conditions using reanalysis data. In section 2.2, we suggested a few conditions in which computing instantaneous fluxes with a 1°C change in SST was sensitive to the inputs. Here we aim to provide a broader perspective on how potential biases or uncertainties in the input affect the diurnal warming model and at what point do they become important. This section will evaluate the effects of potential errors within the primary contributors, such as wind, radiation, and precipitation, of the POSH model.

5.1 Point Sensitivity Study

Diurnal warming develops as a result of primarily low wind speed and large solar heating. It is important to recognize that potential biases and/or measurement error in the wind or radiation fields will then impact the model results differently, depending on their magnitude and diurnal variability. To demonstrate this, model simulations of POSH's dSST response are computed for ranges in wind speed and maximum solar radiation at a given point, similar to that used by Gentemann et al. [2009]; the model runs are computed for a 24 h day in which wind speeds are held at a constant value and the solar radiation is interpolated from a bell-curve function using the peak value to simulate a real solar diurnal cycle. The winds range from 0.2 to 10.2 m/s with an interval of 0.2 m/s, and the solar radiation maximums range from 500 to 1200 W/m2 with an interval of 10 W/m2. All other parameters are set to fixed values typical for the tropics with near-neutral stability, foundation sea surface temperature = 20°C, air temperature = 19°C, pressure = 1020 hPa, specific humidity is computed as given in section 2.2.1, and rain is neglected. In addition, responses of latent and sensible heat flux are also computed when dSST is at a maximum. For each combination of wind and peak radiation, the peak diurnal warming magnitudes over the course of the day are plotted in Figure 8. The results indicate that the diurnal warming magnitude is weak (between 0°C and 0.2°C) at wind speeds >5 m/s without significant heating from the sun, and maximum warming >1°C occurs only when winds are typically <3 m/s at any realistic solar energy range.

Details are in the caption following the image

Sensitivity study of peak diurnal warming magnitudes generated by POSH from a 24 h model simulation as a function of wind speed and maximum solar radiation. Foundation sea surface temperature is 20°C, air temperature is 19°C, wind speeds are held constant throughout the day, maximum solar radiation represents the peak of a realistic bell-shaped solar cycle.

When assessing the response of diurnal heating in these model simulations, note first that there is no wind variability within the 24 h period. In the presence of solar heating, the wind diurnal variability is crucial to understanding the full range of heating. Patterns or trends of actual diurnal wind variability are quite endless and it is difficult to choose one specific trend for this simulation. We can approach the results in Figure 8 as example of diurnal warming in the case of low wind variability. While this is not ideal, it still demonstrates that the effects of radiation and winds on the maximum dSST are both asymmetric about the mean of their respective ranges. This means that certain ranges of radiation and wind will have dramatically different effects on diurnal warming than others. For instance, any error correction in which winds are above 3 m/s is less likely to change the maximum diurnal warming under these conditions. In this case, with 5 m/s wind speeds, the diurnal warming is quite negligible and the variations in SSTskin behave similarly to the SSTdepth [Kawai and Wada, 2007].

The latent heat flux differences taken at the time when dSST is maximum are shown in Figure 9 (left). Assuming near-neutral conditions greatly limits the amount of latent heat flux and the estimates shown here are considered a lower limit. A peculiar feature of the latent heat flux response is the sharp maxima at wind speeds roughly below 1 m/s and decrease in the magnitude of latent heat flux difference below that. As discussed in section 2.2, the change in latent heat flux observed is always positive, but dependence of latent heat flux on the humidity and wind speed is such that a cutoff exists in the rate of change for winds below 1 m/s. The direct response of latent heat flux is proportional to changes in wind spend: a decrease in speed will decrease the latent heat flux. However, decreasing winds also favor diurnal warming and diurnal warming then causes changes in stability and thus surface humidity. The paradox between the diurnal warming model and flux model setup under low wind speed conditions and small humidity gradients is that the most extreme cases in diurnal warming may not impact latent heat fluxes as significantly as those with slightly stronger winds around 1 m/s. Additionally, the decrease in the magnitude of the flux difference is less likely to show up in the model output because the low wind speeds are likely to be flagged when wind stress is below the set threshold. Further attention to this topic is needed in the future.

Details are in the caption following the image

Same as Figure 8 except with (left) latent heat flux difference and (right) sensible heat flux differences when dSST is maximum.

Sensible heat flux differences, on the other hand, resemble changes to SST. Temperature and winds are roughly linearly related in the parameterization for sensible heat flux, so the characteristic maxima in the latent heat fluxes is considerably less evident in the sensible heat flux response (Figure 9, right).

5.2 Wind Sensitivity in POSH Data Sets

From the sensitivity study described in section 5.1, we know that POSH-modeled diurnal warming is more sensitive to changes in wind speed, particularly under 3 m/s, than to radiation under near-neutral conditions; the extent of the sensitivity of diurnal warming on daily and seasonal scales is of particular interest. Furthermore, inherent errors in the MERRA wind fields will likely influence dSST and flux biases on a variety of spatial and temporal scales, so it is important to evaluate to what degree an error in the MERRA wind fields will affect POSH-modeled diurnal warming under a wide variety of conditions.

Roberts et al. [2012] conducted a comparison between MERRA and in situ bulk variables (air temperature, sea surface temperature, surface and air specific humidity, and wind speed) from the SEAFLUX data set by Curry et al. [2004]. The wind speed comparison, in particular, showed that MERRA had an overall positive bias for the entire distribution of wind speeds. Using the information from Roberts et al. [2012], a best guess estimate of a bias correction is determined. Applying a best fit line correction is not ideal because wind validation with in situ measurements is problematic for several reasons (including mechanical limitations and vector quantity scaling), and the reliability of best fit lines in the low wind regimes, particularly <1 m/s, are questionable at best. However, the mean MERRA-in situ difference of 0.69 m/s can be used to represent a systematic bias value in the MERRA winds.

The mean difference from Roberts et al. [2012] is used here to adjust wind speeds and create a new, best guess bias-corrected sample of diurnal warming and fluxes for a sample 2 month period, January through February 2002. Using a sample time period helps evaluate the impact of a bias on dSSTs and fluxes without the computational expense of recomputing the entire data set. A single, constant bias correction will not suffice for winds below the adjustment value; the resulting low wind speeds will be physically inconsistent negative values. Instead, all winds are adjusted using a modified bias correction computed from a hyperbolic tangent function to smoothly adjust winds that occur between 1.5 and 0.0 m/s (Figure 10).

Details are in the caption following the image

Comparison of original MERRA wind values with two bias-corrected wind values. A one-to-one line (dotted), in which MERRA winds are equal to the modified winds, is given for reference. The first bias correction (dashed) is a systematic adjustment of a 0.69 m/s decrease for all wind speed values. The second (solid line) is an adjusted bias corrected to all wind speeds using a hyperbolic tangent function multiplied by the systematic adjustment. The value of the bias correction can be found by subtracting the y-coordinate value of a point on the red line from the x-coordinate value at the same point.

By adjusting the winds, the majority of the oceans experience a difference between the bias corrected and orginal wind speed dSST of generally <0.2°C on a daily scale, while small, isolated differences can be as large as 1.2°C. As an example of the bias-corrected wind effect, each day's diurnal warming is broken down into each dSST's respective wind ranges from 0 to 5.5 m/s for all days in the 2 month period. To determine which wind speed range's dSST is most affected, exceedance probability curves are computed for the original MERRA and adjusted wind speed dSSTs are computed for each wind speed range. The value of a point on the exceedance probability curve represents the probability that, for a given wind speed range, a random value in the diurnal warming data set is less than or equal to the corresponding dSST magnitude on the x-axis. Therefore, for a given dSST threshold value, lower probabilities on the exceedance curve correspond to a better likelihood that the data contain larger dSSTs than the given threshold value. The differences of the exceedance curves between the original and bias-corrected dSST's (Figure 11) are all positive, meaning the wind adjustment is increasing diurnal warming at all wind ranges. While the exact probability values can vary from day to day, the general pattern is similar for all days in the 2 month period, and the peak difference between the dSST probabilities of all wind ranges for the majority of the days occurs when winds are between 1.5 and 2.5 m/s. This peak is consistent with the lowest wind speed ranges with the largest bias correction from Figure 10, though this might not be surprising since the change in dSSTs at lower wind speeds are expected to be most sensitive to small changes in wind speed. At dSST thresholds >2.25°C, the difference in probabilities between wind ranges below 1.5 m/s converge to similar values; the change is a result of a trade-off between decreasing winds and a decreasing bias adjustment. However, while the bias adjustment is reduced by a half or more in the wind speed range between 0.0 and 0.5 m/s, a observable shift in the distribution of diurnal warming above 2°C can still be noted, as more gridpoints display heating above 3.5°C at a time when the original data set displayed none.

Details are in the caption following the image

POSH dSST exceedance probability difference curves for different low wind speed ranges between 0 and 5 m/s on 8 January 2002. The probability difference is computed by subtracting the exceedance curves of dSST with bias-corrected MERRA wind from the dSST exceedance curve with the original winds for each wind speed range.

Bimonthly average differences for the sample 2 month period are computed between the new, adjusted wind speed data set and the original (not shown). During this period, the majority of the bimonthly average dSST differences do not exceed 0.06°C. This is not surprising as the global average diurnal warming amplitude is much smaller than the occasional large warming events exceeding 3°C. However, the largest differences are only around one-tenth of a degree in places where the stronger heating “hotspots” are located and are still relatively close to the desired accuracy threshold in sea surface temperature. Since the changes between the original and wind adjusted data sets are comparatively small, the general spatial locations of diurnal warming are consistent with the bimonthly composites of dSST during the same time period. The spatial distribution of the sensible heat flux and latent heat flux differences are quite similar and the magnitudes are <0.4 and 2 W/m2, respectively. Overall, these findings are encouraging for subdecadal climate applications [e.g., Bourassa et al., 2013] because POSH model results using MERRA inputs over a 2 month period are not substantially altered by the bias correction applied to the wind fields.

5.3 Precipitation Sensitivity

Precipitation and diurnal warming are interwoven complex processes that occur on multiple scales, particularly in the tropics. Precipitation also influences diurnal warming's growth by modifying ocean and atmospheric stability and kinetic energy budgets. For example, clouds producing precipitation reduce the amount of solar energy transmitted to the surface by reflecting and absorbing energy in the atmosphere. As the rain falls, it may also modify the local air-sea humidity gradients. Precipitation's interaction with the ocean surface depends on its impact rate, horizontal momentum, and temperature [Soloviev and Lukas, 2006]. Small droplets that do not overcome ocean surface tension accumulate as a freshwater lens on top of the ocean whereas larger droplets with higher terminal velocities penetrate the water surface and mix into the column [Soloviev and Lukas, 2006]. In both cases, increased buoyancy and reduced near-surface salinity occur with the influx of freshwater [Gosnell et al., 1995]. In addition, the horizontal transport of falling precipitation from airflow can alter surface roughness and impart horizontal stress on the ocean surface [Shinoda and Hendon, 1998; Soloviev and Lukas, 2006]. However, it is not clear whether precipitation's overall contribution promotes or inhibits diurnal warming. According to Gosnell et al. [1995], rainfall will almost always cool the ocean in the immediate time and vicinity with the assumption that the rainfall temperature does not exceed the wet-bulb temperature at sea level. Gosnell et al. [1995] described the effect of precipitation in terms of an additional sensible heat flux called rainfall sensible heat flux (herein referred to as RSHF) in which the total heat in the ocean is reduced by cool, freshwater mixing into the upper ocean. They showed that during strong rainfall events, the RSHF from individual precipitation events can be twice as large as the turbulent sensible heat flux (or equivalent to the latent heat flux); in one case, with a rainfall rate of 36 mm/h, the RSHF is over 200 W/m2. Overall, these large precipitation events are physically significant but sparse; they found the average sensible heat loss from rainfall in the TOGA COARE region to be much smaller with a value of 2.5 W/m2. While the effect of RSHF on diurnal warming is not explicitly stated by Gosnell et al. [1995] and Fairall et al. [1996b] used the RSHF parameterization in COARE2.5 to compute its contribution to the total heat flux and diurnal warming. Heat loss from the ocean incidentally reduces the accumulated energy within the water column and subsequently weakens the surface heating response. However, Webster et al. [1996] showed that reduced salinity and buoyancy from precipitation actually enhanced diurnal warming more than it subdued warming from heat loss. Similar results were reported by Soloviev and Lukas [1997] who used temperature profiler data in the eastern tropical Pacific, where the ocean experienced light winds and a freshwater lens. Webster [1996] also emphasized that enhancement of diurnal warming from precipitation depends heavily on the timing of the rain event. Additionally, the contribution of precipitation was the smallest of their chosen parameters used to develop an empirical diurnal warming model, and accounted for a mean maximum effect of only 0.3°C.

The following section will describe the effects of precipitation as it is applies to the POSH model. Since POSH is primarily derived from the COARE2.5 model, the discussion of the effects of precipitation on diurnal warming will focus on the theory from Gosnell et al. [1995], particularly on whether the reduced heat flux actually occurs in POSH.

To test the influence of precipitation in the model, new subsets of POSH-modeled diurnal warming are created without rain for January-February and July-August over the 5 year period and comparing them to the original data set on a daily and bimonthly time scale. Comparisons of data with and without precipitation yield contradictory results; under certain conditions, roughly 15% of grid points in every daily file contain dSSTs warmer computed with precipitation than without precipitation. The increase is found to be a result of the integration threshold of heating in the ocean column. The model requires that a total of 50 W/m2 of heat be accumulated in order for the model to begin computing a diurnal warm layer. Whether the deficit in energy amounts to tens or tenths of a watt per square meter, the model will not compute surface warming when it remains below a finite threshold. Evidence of the integration threshold influence is observed when differences between the original, no-precipitation model run (herein referred to as NPMR) and the precipitation model run (herein referred to as PMR) are negative. As discussed above, precipitation lowers the heat content residing in the water column. In theory, compared to the original PMR, the NPMR would have larger dSSTs because it has accumulated more energy without reduced heat from precipitation. For the negative cases, the accumulated energy in the water column for the NPMR is always greater than or equal to the PMR, as is consistent with the theory. However, the initialization of the diurnal cycle is changed, depending on the accumulated heat for each case. At times when the PMR begins to integrate 1 h later than the NPMR, the NPMR had already computed a dSST to which heat is released to the atmosphere and therefore had more outgoing energy. The PMR, on the other hand, retains all energy and accumulates it to the next time step. Therefore, the PMR has accumulated more energy which makes the surface respond with a greater magnitude at each time step until it catches up the NPMR (Figure 12).

Details are in the caption following the image

Differences in the time series of diurnal warming magnitudes on 20 January 2002 at 28.325°S, 73.125°E, for a model run that compute dSSTs with the inclusion of a precipitation rate (PMR) and a model run that neglects precipitation (NPMR).

Details are in the caption following the image

Locations of erroneous dSSTs above 10°C.

The integration threshold is not directly related to the precipitation rate but can affect diurnal warming at all ranges of rain rates. For the time series in Figure 12, a daily average rainfall rate of 0.026 mm/h contributes to a RSHF of only 10−2 W/m2, creating a deficit of 0.08 W/m2 below the integration threshold of total accumulated heat. While these small values of heat flux could be considered negligible on their own, the SST difference between the two model runs of 0.36°C is not. The overall effect is that precipitation increases diurnal warming during the beginning of the diurnal cycle which appears to make it inconsistent with the theory of Gosnell et al. [1995].

Averaging the precipitation effects on diurnal warming over a 2 month time period, conversely, results in differences less than hundredths of a degree. The minute differences are reasonable given that variations in the distribution and frequency of precipitation rate over the time period are substantial, even within the tropics, and when averaged, the relative impact appears to be reduced.

Overall, this example emphasizes that under certain conditions, the model configuration may exaggerate precipitation's influence on diurnal sea surface temperature heating on subdiurnal periods. This inherently decreases the level of confidence in the diurnal warming estimates in section 3, especially in the tropics, where bursts of afternoon convection can be preceded or followed by ample sunshine or where large convective systems block solar radiation from reaching the surface. Interestingly enough, if precipitation does in fact increase the stability by means of a freshwater flux, then additional validation can perhaps be used to further quantify the errors relating to the impact of the integration threshold.

6 Summary and Discussion

A data set of diurnally varying sea surface temperatures is created using a modified version of the Profiles in Oceanic Surface Heating (POSH) model to understand the impact on fluxes over daily and seasonal scales. MERRA atmospheric and radiation data, as well as Reynolds OI sea surface temperature and ice concentration data, are prescribed into the model to forecast hourly diurnal warming magnitudes of the sea surface and sensible and latent heat fluxes over a 5 year period from 2000 to 2004. Diurnal warming magnitudes are limited to 10°C to eliminate the number of cases of erroneous diurnal warming in locations with near-neutral air-sea differences, wind speeds generally below 1 m/s, and ice concentration interference. Erroneous dSSTs, however, are <0.001% of the total data. Diurnal warming magnitudes and fluxes are analyzed on daily and bimonthly scales to identify key characteristics and to compare with other diurnal study results. On a daily scale, POSH estimates of dSSTs can be as large at 6°C, though such occurrences are rare. Often within the tropics and midlatitudes, diurnal warming develops into long bands in the ocean under light surface winds, usually in association with prevalent weather patterns (e.g., high-pressure systems) or some geographic obstruction (e.g., mountains). Characterizing the spatial and temporal placement of large diurnal warming events, like these streaks, using modeled output may be of some assistance to future diurnal warming endeavors that seek to capture sophisticated data observations in the presence of large diurnal warming and determine its influence on short-term, small-scale ocean features (diurnal ocean jets, ocean temperature fronts, etc.) (A. Jessup, personal communication, 2011). The POSH model estimates of diurnal warming on longer (seasonal) time scales effectively replicate general areas of large diurnal warming found the tropics (ITCZ and Indian Ocean) that are consistent with other studies. Although diurnal warming is commonly studied and observed in the tropics, the percentage of hours in which diurnal warming exceeds a threshold (0.67°C in this case) in the midlatitudes and tropics is comparable over the late summer season. At times, the midlatitudes experience greater diurnal warming amplitudes than the tropics. Averaging dSSTs and fluxes over a 2 month period for all 12 months reveals that >30% of the North Atlantic and North Pacific experiences diurnal warming greater than or equal to one-tenth of a degree during July and August. In the same areas, differences between latent and sensible heat fluxes with and without a diurnally varying SST are underestimated by 4 and 0.5 W/m2. During the active monsoon phase in the Indian and Pacific oceans, average latent heat flux differences are as large as 8 W/m2. A different perspective in analyzing persistence of diurnal warming is to compute the percentage of occurrence in which dSSTs and fluxes exceed a value. Up to 25% of the time over July and August, SSTs and latent heat fluxes in the Pacific and Atlantic Oceans can be underestimated by ∼0.7°C and 10 W/m2, respectively. The percentage is even higher in places where bimonthly average dSSTs are consistently large in the tropical western Pacific. Differences in fluxes in excess of 10 W/m2 are commonly considered nonnegligible to the atmosphere. Therefore, diurnal warming underestimates fluxes that are considered important for climate and other applications that are sensitive to fluxes and air-sea energy budgets. It would be interesting for future studies to determine what effects, if any, diurnal warming would have on synoptic-scale weather phenomena in the midlatitudes.

Possible uncertainties of the POSH model are presented by looking at the sensitivity of the model under different wind speed, radiation, and precipitation conditions and by an example of model verification compared to satellite SSTs. Though the sensitivity studies are not completely comprehensive for all conditions, it useful for future users to know certain examples of POSH's strengths and weaknesses. The results in section 5 show that biases in wind and effects of precipitation specifically are less important on seasonal time scales, most likely because the global average of diurnal warming and precipitation are relatively smaller than isolated maximum values found. Because diurnal warming affects surface heat fluxes, flux differences are also examined with the same variables. By assigning a range of solar radiation maximums and wind speeds from 500 to 1200 W/m2 and 0.2 to 10.2 m/s, diurnal warming is projected for a 24 h period under near-neutral conditions and no wind diurnal variability. Maximum dSSTs over the 24 h period are most affected by wind speed and radiation as they increase continuously when wind speed decreases and radiation increases. The rate of increase is largely dependent on the specific magnitudes of winds and radiation, though the specific ranges will change depending on stability and humidity gradients of the ocean and atmosphere, among other things. Similar results are found for the dependence of sensible heat fluxes at dSST maximum near-neutral conditions. On the other hand, latent heat flux differences differ in that the rate of increase below 1 m/s actually slows because of the parameterization dependence on wind speed and specific humidity under near-neutral conditions. Resolving the contradiction between low wind speeds and latent heat fluxes is of great importance for diurnal warming studies; future observational missions that can help validate the relationships between diurnal variability of SSTs and fluxes particularly at low wind speeds <3 m/s would be greatly beneficial for future modeling ventures. One limitation of this study is that feedbacks including air temperature modification from diurnal warming has not been considered and could bound the results by reducing the air-sea temperature differences. This could also be problematic as the near-neutral transfer coefficients are not fully resolved in the flux model where sharp peaks in the contours of latent heat flux are evident in the between slightly positive and slightly negative air-sea temperature differences. Wind speed influences on diurnal warming and fluxes are further investigated by adjusting the MERRA wind speeds by a bias correction using the mean model-in situ difference from Roberts et al. [2012]. On a daily time scale, wind speeds between 2 and 2.5 m/s experience the greatest increase in diurnal warming with the bias correction applied. On a bimonthly scale, the changes are less noticeable, again likely because of the relatively low global average magnitudes of diurnal warming. Precipitation is examined in a similar manner: a sample data set spanning two bimonthly periods is compared to the original data set. In the case where precipitation is present, there are periods of time in which the calculation of diurnal warming is affected by the configuration of the model in that the heat content of the ocean falls below the integration threshold; thus, the code accumulates the heat and continues to the next time step without calculating a warm layer. When a nonprecipitation model run surpasses the threshold and the precipitation model run does not, the delay causes the precipitation model run to have larger diurnal warming. When a diurnal warm layer is computed, more energy is released out of the water column than from precipitation. Thus, when the precipitation model run is delayed in computing diurnal warming, the temperature responds to more energy contained in the column. The result is that precipitation will cause the model to produce higher dSSTs with precipitation than without. This is a potential major source of uncertainty in the model because precipitation affects diurnal warming in the POSH model by means of only reducing the sensible heat flux. The comparison of diurnal warming events larger than 0.5°C in POSH to SEVIRI hourly satellite data over a few sample dates in January, March, July, and October of 2009 show that, on average, POSH overestimates the peak of the diurnal cycle and the decay near or after sunset. While the nighttime decay is not a problem isolated to POSH, it potentially introduces error in the results of persistence of diurnal warming presented in section 3.3 in that diurnal warming may actually persist longer than what is shown but the overall magnitude may be overestimated. Additionally, it is interesting to note that the solar absorption profile was modified so absorption was increased by 20% and justified by the regional observations used in Genteman et al. [2009]. Given the consistent overestimation, the choice to increase the solar absorption profile may be a potential error source for POSH, though a more comprehensive comparison is required for verification. The SEVIRI data set is an ideal data set for diurnal warming studies in that the retrievals are consistent between day and night and it contains hourly observations over the course of the day. It is vital that data producers acknowledge that studies on diurnal variability of sea surface temperatures require validation SSTs from satellite that exhibit roughly 100% diurnal sensitivity in order to produce accurate comparisons with modeled diurnally varying SST data sets. A current effort is underway to reprocess the SEVIRI data with alternative retrieval method outlined in Merchant et al. [2013] that will produce SEVIRI SSTs with explicit diurnal sensitivity. The production of high quality, diurnally varying SST products from satellite observations and modeling studies should be used in tandem to further our understanding of diurnal variability.

Acknowledgments

This work was supported by the NASA NEWS program and NOAA/COD. We thank Chelle Gentemann for her comments. We would also like to acknowledge Chris Merchant and two other anonymous reviews for their helpful suggestions and comments. The data produced in this study are not publicly available as of the publication date but can be downloaded via request by contacting the authors.

    Appendix A: Erroneous dSSTs and Wind Stress Threshold

    Initial POSH-modeled diurnal warming using the basic COARE2.5 bulk flux routine produced erroneous dSSTs, defined as diurnal warming >10°C, that are unrealistic in the real world. The total number of grid points that exhibit erroneous dSSTs in the 5 year data set is <0.001% of the total number of ocean data points, but they interfere with the spatial and temporal averaging analysis. Grid points that display erroneous dSSTs are located in areas which wind speeds are generally equal to or <1 m/s, air-sea temperature differences are positive (stable), and model iterations that compute wind stress does not converge to a single value. The wind stress decreases with each iteration until enough heat has accumulated over the time step to activate the calculations for a diurnal warm layer. With a wind stress of virtually zero, the diurnal warming and fluxes increase nonlinearly. This is a well-known problem in bulk models since the parameterizations are not fully capable of resolving fluxes under completely calm and stable conditions [Fairall et al., 1996b]. A second bulk flux model (BVW06) from Bourassa [2006] is used in an attempt to reduce erroneous dSSTs, as well as computational time, but only slight improvements are made to the dSSTs. Next, a threshold on the wind stress is incorporated into the BVW06 routine to remove locations in which the wind stress iteratively approaches zero. Over a 2 month time period, the threshold decreases the number of erroneous dSSTs by 6%. After the implementation of the wind stress threshold, spatial maps of erroneous dSSTs are used to identify regional errors (Figure A1).

    The majority of erroneous diurnal warming counts over the entire 5 year data set occur in the high latitudes. Moreover, larger counts of unreasonably large diurnal warming are found in the winter polar latitudes when the counts are analyzed by season. We suspect that discrepancies between MERRA's air temperature and Reynold's sea surface temperature and sea ice concentration at locations near ice is a potential cause of large diurnal warming produced by the model. The combination of positive air-sea stability in and near the presence of ice and low wind speeds is likely causing the divergent calculation in wind stress but warrants further investigation. It has also been suggested that the improvements made in version 3 of the COARE algorithm may remedy this issue, though the new algorithm has not been tested in this work.

    Appendix B: Updated Subroutines and Corrections

    B1. Solar Insolation and Solar Zenith Angle

    The COARE2.5 flux routine for POSH was updated with the inclusion of a solar zenith angle that is used to adjust the amount of solar radiation entering the ocean beneath the surface. However, the solar angle subroutine provided did not resolve angles globally. Therefore, the calculation for solar zenith angle is updated using the algorithms for longitude angle and declination angle at the top of the atmosphere for all locations. Solar insolation (top of the atmosphere) can also be calculated using solar zenith angle and is included in the code for completeness.

    B2. Hour of Dawn

    To run the POSH model beginning at local dawn, it is necessary to calculate when local dawn occurs. The author of POSH has updated the hour of dawn calculations (C. Gentemann, personal communication, 2010), but a different algorithm is used herein to suit our needs for specific data processing. MERRA data are given in terms of UTC; therefore, the values of time are changed from UTC to local and back to UTC using an algorithm provided by the Nautical Almanac Office [1989]. The algorithm computes the hour of dawn and dusk for all locations; for polar latitudes that experience 24 h daylight or darkness, the nearest latitude's dawn and dusk values are used. It is possible that local dawn and dusk may occur on a different date in UTC. Therefore, the dawn and dusk are corrected using longitude so that local time corresponds to the correct date in UTC. The hour of dawn is rounded down to the nearest integer corresponding to the nearest whole hour. Another hour is subtracted from the dawn integer to give the model an additional hour to initialize.