The erosion of Saharan soil is the World's largest annual source of mineral dust aerosols, resulting in a deposition of more than 40% of the global atmospheric dust into the North Atlantic (NA). By changing the atmospheric opacity, mineral dust can alter the shortwave radiative forcing at the surface of the ocean, altering the ocean mixed layer heat budget and therefore affecting the sea surface temperature (SST). Moreover, changes of the total amount of energy received at the ocean surface have an impact on the ocean circulation. In this thesis we combine several satellite observations, in-situ radiation measurements, a 1D mixed layer model of the ocean, and various versions of a 3D general ocean circulation model, to study the impact of Saharan dust on the circulation of the NA. A buoyancy source generated by realistic dust-induced shortwave flux anomalies is imposed in the eastern NA and the differences between this simulation and an unperturbed one are investigated in terms of the ocean dynamical adjustment and changes in the Atlantic Meridional Overturning Circulation (AMOC). A joint analysis of aerosol optical depth retrievals from the MODIS sensor and SST from the TMI sensor for the period 2000-2006 shows a decrease in SST of 0.2° to 0.4°C simultaneously with, or shortly after, strong dust outbreaks, which is consistent with an independent estimate of SST decrease simulated by a local 1D mixed layer model. A comparison between observed TMI SST fields and simulated SSTs with an eddy-permitting model of the NA suggests a local cooling of about 0.5°C on sub-seasonal to interannual time-scales. Results of the 3D simulations show that an advection of the ocean properties ocurs in response to the buoyancy source in the eastern subtropical NA. The eddies and baroclinic instabilities present in the ocean advect the signal towards the west and back towards the east. Once they have reached the African coast, they trigger westward propagating Rossby waves. The time-mean differences of AMOC between the perturbed and unperturbed simulations show an increased meridional transport at 38°N and 43°N of 0.55 and 0.45 Sv, respectively, and a decreased AMOC at 40°N and 45°N of 0.2 Sv. We conclude that the effect of Saharan dust should be incorporated in ocean numerical simulations, specially under the frame of climate change studies when a changing dust load of the atmosphere in response to a changing climate could be possible.
Contents
1 Introduction
1.1 Aims
1.2 Structure
2 Remote Sensing: SST, AOD. KPP-1D. MITgcm
2.1 Introduction
2.2 Data and Methodology
2.2.1 MODIS AOD
2.2.2 TMI SST
2.3 Aerosol Radiative Forcing during AEROSE-I
2.4 Observed SST and AOD anomalies
2.5 Simulated SST anomalies in the ocean mixed layer
2.6 Isolating dust-induced SST anomalies
2.6.1 Model description
2.6.2 Model setup
2.6.3 Results from 3D eddy-permitting simulation
2.7 Concluding remarks
3 Impact of Saharan Dust on the North Atlantic Circulation
3.1 Introduction
3.2 Methods
3.2.1 The experimental setup
3.2.2 Construction of a realistic perturbation
3.3 Mean ocean circulation
3.4 Perturbed response
3.4.1 Large-scale response
3.4.2 Sub-basin and local response
3.4.3 Vertical structure of temperature anomalies
3.4.4 Meridional Overturning and Heat Transport in the Atlantic
3.5 Discussion and Conclusions
4 Conclusions
4.1 Summary
4.2 Outlook
Acronyms
List of Figures
List of Tables
Bibliography
Acknowledgements
Chapter 1
Introduction
Mineral dust and aerosols originating from wind-induced erosion of soil in arid regions can impact the climate system in many ways, e.g., by altering weather or by affecting atmospheric chemistry. As an example, mineral dust and the very dry Saharan Air Layer (SAL), with which it is associated, have been shown to affect the development of clouds and precipitation, as well as modulating thunderstorm activities and tropical cyclogenesis (Sassen et al., 2003; Dunion and Velden, 2004; Yoshioka et al., 2007; Wu, 2007; Evan et al., 2008). Mineral dust, in particular, by increasing the attenuation (scattering and absorption) of solar radiation in the atmosphere, leads to a redistribution of radiative heating from the surface upward into the dust layer (e.g., Miller and Tegen, 1999) and to a decreased shortwave irradiance at sea level. By changing the atmospheric opacity, mineral dust can thus alter the shortwave radiative forcing at the surface of the ocean (Jickells et al., 2005; Evan et al., 2009); in addition, thermal emissions from dust aerosols can increase the surface longwave forcing (Vogelmann et al., 2003; Zhu et al., 2007). Both processes play a role in the ocean mixed layer heat budget and can therefore affect the climatologically important sea surface temperature (SST).
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Figure 1.1: Schematic of the biogeochemical and physical response to dust deposition from the project ”Surface Ocean Processes in the Anthropocene (SOPRAN)” (SOPRAN proposal, unpublished, 2006).
In principle, the ocean circulation and transport properties can also change in response to enhanced mineral dust or aerosol concentrations. The inhomogeneous distribution of dust aerosols in the atmosphere will lead to a differential heating at the surface. As a result, horizonal gradients of density would be generated, which in turn would change the ocean currents and ultimately, the ocean circulation (Marzeion et al., 2005).
Moreover, once settled to the oceans surface, mineral dust can act as a fertilizer, either directly or via stimulation of nitrogen fixation (Mills et al., 2004; Moore et al., 2009), and potentially can enhance biological productivity and thereby potentially can change the composition of phytoplankton (Erickson et al., 2003; Coale, 2004; Boyd, 2007; Blain et al., 2007). Changes in productivity can, in turn, feed back on the atmosphere through altered trace gas emissions. Hence atmospheric impacts on the ocean represent Earth System linkages with potentially major implications for future atmospheric CO2 levels, marine ecosystem behaviour and atmospheric chemistry. See Fig. 1.1 for a schematic representation.
As compared to the rest of the World, the erosion of the Saharan soil is by far the largest annual source of mineral dust aerosols (Prospero et al., 2002; Washington et al., 2003). Fig. 1.2 shows the distribution of the dust fluxes to the Earth surface published by Jickells et al. (2005). The figure is based on a composite of three published modeling studies that match satellite aerosol optical depth, in-situ concentrations, and deposition observations of dust (Ginoux et al., 2001; Mahowald and Luo, 2003; Tegen et al., 2004) and appears to match observations well. The dust inputs to the oceans result in a deposition of more than 40% (200-260 T g yr−1 ) of the global dust into the North Atlantic Ocean (see also, Kaufman et al., 2005; Mahowald et al., 2005, and references therein). Dust transport over the ocean affects atmospheric radiation transfer and hence the quantity and quality of light entering the surface ocean.
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Figure 1.2: Dust fluxes to the world oceans from Jickells et al. (2005). Total atmospheric dust inputs to the oceans = 450 Tg year−1. Percentage inputs to ocean basins based on this figure are as follows: North Atlantic, 43%; South Atlantic, 4%; North Pacific, 15%; South Pacific, 6%; Indian Ocean, 25%; and Southern Ocean, 6%.
There is plenty of bibliography describing the properties of Saharan dust (see for ex- ample Schepanski et al., 2009a, and references therein). What matters to this work are its seasonality and its storms/outbreaks, which are also in close relation with its hori- zontal distribution. Fig. 1.3 shows an example of a dust plume over the Sahara Desert and expanding over the Atlantic Ocean and Canary Islands, from the Total Ozone Map- ping Spectrometer (TOMS1 ). The land sources of this dust plume are clearly visible, with the main source coming from Western Sahara, Mauritania and the Sahel. There are several potential inland source areas for the dust over the ocean. These areas show seasonal changes dust source activity that are related to seasonal changes in meteoro- logical conditions (Schepanski et al., 2009b). For example, the Bodélé depression is the most active source during winter and accounts for up to 50% of the dust found in the Cape Verde archipelago (Koren et al., 2006; Schepanski et al., 2009a) During the dust transport towards the Atlantic Ocean, the dust plume can remain near the surface and be observed as a dust storm (Fig. 1.3), or can be transported as elevated layer (Kalu, 1979). The elevation of the dust layers in turn, depends on the season. In winter/spring the dust transport occurs mostly in near-surface layers, while in summer the transport is at higher layers. Remote sensing retrievals can be used to determine dust fluxes into the North Atlantic. The Aerosol Optical Depth (AOD) is a measure of the degree to which aerosols prevent the transmission of light. It is a measure of radiation extinc- tion due to aerosol scattering and absorption and is available at different spectral bands from different instruments. We use here AOD at 550 nm from the Moderate Resolution Imaging Spectroradiometer (MODIS2, more details are provided in Chapter 2). While AOD values of 0.2 correspond to a clear day, for AOD values of about 4 one would have difficulty seeing the sun in the middle of the day.
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Figure 1.3: Aerosol Index (AI) distribution in the eastern North Atlanic, from February 26, 2000, obtained from the Total Ozone Mapping Spectrometer (TOMS). The green to red false colors represent increasing amounts of aerosol. The AI is an adimensional quantity.
The time-mean distribution of MODIS AOD averaged over the period 2000-2006 for the summer months and the winter months of the northern hemisphere displayed in
Fig. 1.4, shows obvious differences in amplitude and in the horizontal path between the seasons. We can identify: 1) the high-dust summer plume located between 15◦ N and 25◦ N, and 2) the low-dust winter plume extending between 5◦ S and 15◦ N. The Saharan dust’s annual variability is even more obvious from the time series taken right off the African coast shown in Fig. 1.4c. Superposed to the seasonal variability of the dust, are the dust outbreaks. These are characterized by high concentrations of dust in the atmosphere lasting over a short period, from only a couple of days up to one week. The Saharan dust outbreaks over the North Atlantic are usually seen right off the African Coast from the Cape Verde archipelago up to 35◦ N (see Fig. 1.3 as an example).
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Figure 1.4: Mean geographical distribution of MODIS Aerosol Optical Depth (2000- 2006) for (a) the high-dust months June/July/August, (b) the low-dust months November/December/January and (c) time series of weekly AOD (in blue) jointly with monthly means (in black), for the period 2002 - 2006, averaged over 30◦ W - 20◦ W; 15◦ N - 25◦ N. The white areas correspond to values of AOD outside the color scale.
Hot dry Saharan air, known as the Sahara Air Layer (SAL), can be traced far over the western Atlantic (Prospero and Carlson, 1981; Colarco et al., 2003) and associated with this layer are often enhanced concentrations of mineral dust. As an example, Lau and Kim (2007) reported a significant increase in Saharan dust over the western North Atlantic during 2006 and argued that this enhanced dust concentration might have been responsible for a cooling of the ocean’s surface there, during the same year, by scattering more solar radiation to space and depriving the surface of some solar heating.
The combined effects of the inhomogeneous distribution of dust in the atmosphere, and the dust-induced cooling in the eastern subtropical North Atlantic, can generate local sub-surface density gradients which, through the thermal wind relation, can result in a changed circulation. In principle, changes from a sub-basin to a basin scale could be possible.
In addition, a cooling in the subtropical eastern North Atlantic can act as a buoyancy source for changes in the transport of mass and heat in the Atlantic. Köhl (2005) inves- tigated the mechanisms and controlling regions that influence the Atlantic Meridional Overturning Circulation (AMOC) by using adjoint sensitivities. The author found the AMOC to be sensitive to anomalies in the eastern part of the Atlantic and, moreover, that changes in temperature, salinity and surface buoyancy in the Canary Basin are of great importance to detect changes in the AMOC. Detecting changes in the AMOC is of interest because this secondary circulation is related to the meridional heat transport in the ocean, which greatly influences the mid- and high-latitude climate in Northern Europe (Hall and Bryden, 1982). In our model work we impose dust-induced density changes at the eastern side of the North Atlantic and seek to study their impact on the AMOC and on the meridional heat transports.
The work presented in this thesis is part of the SOPRAN (Surface Ocean Processes in the Anthropocene, http://sopran.pangaea.de) and international SOLAS (Surface Ocean Lower Atmosphere Study, http://www.solas-int.org/) projects. SOPRAN’s sub-projects consist in the following:
- Theme 1: The oceanic response to atmospheric dust.
- Theme 2: Effect of high CO2 on marine ecosystems and sea-to-air gas fluxes.
- Theme 3: Reduction and emission of radiatively and chemically active gases in the Tropical Oceans.
- Theme 4: Inter-phase transfer at the sea surface.
Our work is developed in the frame of Theme 1. Fig. 1.1 shows a scheme of the biogeochemical response to dust deposition that summarizes the potential impacts of atmospheric dust in the oceans that are being investigated within SOPRAN-Theme 1, and have been discussed above.
Knowing the impact of Saharan dust on the circulation of the eastern subtropical Atlantic and on associated transports of nutrients is therefore specifically important for understanding the climatic relevance of Saharan dust in terms of ocean circulation, airsea interaction, and biological productivity.
1.1 Aims
The main goals and questions addressed in this thesis can be described as follows:
- Look for evidence of ocean surface dust-induced local cooling in the eastern subtropical North Atlantic, by using AOD and SST information from satellite observations.
- Compare SST retrievals to estimate the ocean surface cooling below a dust cloud (TMI, AMSR-E, AVHRR), in order to choose the appropriate one.
- Estimate how much of the observed changes in SST during strong dust outbreaks are dust-related. To this end, a one-dimensional local mixed layer model is forced with the dust-induced anomalies of the shortwave fluxes. Such anomalies are constructed from radiation and AOD measurements taken on board of the trans- Atlantic Aerosol and Ocean Science Expeditions I (AEROSE-I) cruise, so that a realistic simulation is obtained.
- Use of a three-dimensional eddy-permitting general circulation model, to see whether the differences between the observed and simulated SST can be related to Saharan dust, with special focus on its seasonal variability.
- Force a three-dimensional eddy-permitting numerical model of the ocean by per- turbations in solar shortwave flux fields, and compare it to an unperturbed model run.
- Perform a sensitivity study of the MOC reacting to density changes imposed at the eastern subtropical North Atlantic.
1.2 Structure
This thesis is organized in two main chapters where we develop our work, and a fi- nal chapter that includes our general conclusions and outlook. Chapters 2 and 3 are structured with introduction, data and methods, results and conclusion sections.
Chapter 2 includes a combined analysis of satellite AOD and SST in the subtropical eastern North Atlantic, and two numerical simulations: (1) a 1D ocean mixed layer model; and (2) a 3D eddy-permitting general ocean circulation model. The simulation (1) is used to estimate the impact of the dust-induced radiative forcing in the local SST during dust outbreaks in the subtropical eastern North Atlantic. Radiative in-situ measurements taken during a hydrographic cruise in that region are used to estimate the aerosol radiative forcing with which the 1D simulations are forced. The output from the simulation (2) is used to discrimiate dust-induced SST anomalies from dynamically- induced SST anomalies in time- and spatial-scales that (1) is not able to simulate, by comparing it to the TMI SST observations. In addition, a validation of the chosen SST database is carried out by comparing it with other SST satellite products from AMSR-E and AVHRR. The main results shown in this chapter have been submitted to the Journal of Geophysical Research Oceans (see Mart í nez Avellaneda et al.).
In Chapter 3, we present a sensitivity experiment of the ocean circulation to density changes imposed at the eastern subtropical North Atlantic by the dust-induced anomalies on the shortwave fluxes. By forcing a 3D eddy-permitting numerical model with realistic dust-induced perturbation in solar shortwave flux fields, and comparing these model results with an unperturbed simulation, the dust effects on the circulation and transport of ocean properties, the AMOC and meridional heat transport are investigated.
Chapter 2 Response of the eastern subtropical North Atlantic sea surface temperature to Saharan dust
2.1 Introduction
To identify the eastern Atlantic response to Saharan mineral dust one should combine at- mospheric information about dust concentrations with in situ observations of the ocean surface temperature. Unfortunately, direct measurements of sea surface temperature (SST) in the eastern North Atlantic in the form of surface drifter measurements or ARGO near surface measurements are too sparse to come to statistically significant con- clusions. Until now, measurements of radiative forcing are available only at very few locations, e.g., from island stations and some ships, and observations of biological pro- ductivity are only now becoming available in that region through programs like SOLAS (http://www.uea.ac.uk/env/solas/). On the other hand, dust clouds over the ocean can be detected from satellite measurements at visible wavelengths. Analyzing the exist- ing satellite database with respect to dust-induced SST anomalies in the eastern North Atlantic seems therefore an obvious and necessary step to be taken.
An example of a Saharan dust outbreak is shown in Fig. 2.1, illustrating an intense dust storm lasting 5 days during early March 2004, as seen by the Moderate Resolu- tion Imaging Spectroradiometer (MODIS) on board of the US NASA Earth Observing System (EOS) Terra satellite. The figure clearly reveals the large spatial extent of a dust layer, which typically can cover an area of about 550 km in the zonal direction and 1750 km meridionally between the African coast and the Canary Islands. Radiometric measurements taken quasi-simultaneously underneath this dust layer during the trans- Atlantic Aerosol and Ocean Science Expeditions (AEROSE) suggest surface radiative forcing anomalies of approximately -100 W m−2 (Morris et al., 2006), equivalent to a 40% reduction of shortwave heating at the surface. Given these strong negative short- wave heating anomalies, a strong thermal response of the upper ocean to Saharan dust should be expected (a radiative forcing anomaly of -100 Wm−2 over 15 days would cool a 30 m thick mixed layer by approximately 1◦ C).
Previously, atmospheric model simulations had suggested that underneath dense atmo- spheric mineral dust layers the SST may decrease by as much as 1◦ C (Miller and Tegen, 1998). In addition, recent works from Yoshioka et al. (2007), Foltz and McPhaden (2008) and Evan et al. (2008) observe that changes in aerosol cover have a significant impact on the Atlantic SST. Yet, using the existing observational database, a quantitative esti-
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Figure 2.1: MODIS Rapid Response System 2-km resolution true color image off the West Coast of Africa, acquired on March 4, 2004 at 11:55 UTC on board the EOS Terra platform.
mation of how much of the observed ocean surface cooling is dust-induced is still missing. In this chapter we:
1. Perform a simultaneous analysis of several satellite datasets to investigate whether Saharan mineral dust leads to a cooling of SST of the eastern North Atlantic both during strong storms and at seasonal time scales.
2. Quantify how much of the observed SST changes are dust-induced, using for that purpose:
- a 1-dimensional local mixed layer model of the upper ocean;
- a full 3-dimensional eddy-permitting circulation model of the North Atlantic.
While the eddy-permitting model will give us the full perspective of the dynamical changes in SST that can be expected in our study area, the 1D perspective will be used to provide a measure of a local change in SST that can be expected in response to a local dust-induced perturbation.
The remainder of this chapter is organized as follows: In Section 2.2 we describe the data used in the present work. Aerosol radiative forcing anomalies will be shown in Section 2.3. The relation between the observed SST and Aerosol Optical Depth (AOD) anomalies will be discussed in Section 2.4 and numerical simulations of SST anomalies as they should result from observed dust loads are presented in Section 2.5. A joint interpretation of observed AOD and SST anomalies and model simulations of SST is provided in Section 2.6. The concluding remarks are given in Section 2.7.
2.2 Data and Methodology
Our study is based on a suite of parameters measured from satellites between 2000 and 2006, such as all-weather microwave SST measurements and AOD of the atmosphere. In addition, we used several parameters measured during the AEROSE expedition con- ducted from aboard the NOAA Ship Ronald H. Brown in the eastern subtropical North Atlantic.
2.2.1 MODIS AOD
AOD time series provide a measure of Saharan mineral dust concentrations and can be used to compute the anomaly of solar shortwave irradiance at sea level underneath the dust layer. Daily estimates of AOD are available from the MODIS instrument on board the Terra and Aqua satellites (Remer et al., 2005, 2006). These data are used here to determine the frequency and intensity of Saharan dust outbreaks over the eastern subtropical North Atlantic, as well as to estimate the associated anomalies in solar forcing of the ocean. For our study we used the daily gridded AOD Level-3 MODIS Terra Collection 5 product, available on a 1◦ x 1◦ spatial resolution for the period February 2000 to December 2006 (ftp://ladsweb.nascom.nasa.gov). During the beginning of the dust outbreak event shown in Fig. 2.1, AOD values as large as 4.5 were observed; during its further evolution the main axis of the plume travelled less than a few degrees westward, while its optical depths decreased to 0.5 on March 9, suggesting primarily dry deposition of dust onto the ocean surface (Kaufman et al., 2005; Schepanski et al., 2009a).
Daily global fields of AOD contain gaps that arise due to various reasons (e.g., sun glint, clouds and/or bright underlying surfaces). Dealing with those gaps in our analysis is difficult and to avoid them we produced weekly composites, which still preserve the major Saharan dust outbreaks. The composites were computed by area-weighted averaging of all observations within each of the 1◦ x 1◦ grid cells over a weekly period.
We identified Saharan dust outbreaks, from the daily MODIS AOD product and from the computed weekly AOD anomalies (relative to a climatological seasonal cycle), when values exceeded the AOD time-mean plus twice the local standard deviation (< AOD > +2σ > 0.85 and > 0.30, for daily and weekly fields, respectively). From Fig. 2.2, several strong dust outbreaks can be detected during the period 2000-2006 between Cape Verde and the Canary Islands (4 in summer, 7 in winter, 1 in spring and 2 in autumn). It is also obvious from the figure that daily data would lead to much higher AOD values during dust storm events and that some of those are eliminated in the weekly averages. However, because our focus here is primarily on the ocean’s long-term response to dust, the outbreaks with longer duration are the more relevant events and these will still be captured in the weekly averages.
2.2.2 TMI SST
While AVHRR (Advanced Very High Resolution Radiometer) and MODIS infrared (IR) SST retrievals are significantly impacted by the presence of mineral dust in the atmo- sphere, SST retrievals from microwave (MW) radiometry are not (May et al., 1992; Wentz et al., 2000; Chelton and Wentz, 2005). For our study, microwave SST retrievals from
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Figure 2.2: Daily retrievals of AOD (top) and their anomalies for weekly composites for 2000-2006 (bottom) from MODIS, averaged over 21◦ W - 27◦ W; 19◦ N - 26.5◦ N. The horizontal lines represent the < AOD > +2σ threshold value, respectively.
the TRMM Microwave Imager (TMI) radiometer on board the Tropical Rainfall Measur- ing Mission (TRMM) satellite were used as weekly SST fields at a spatial resolution of 0.25◦ over the period January 1998 to December 2006. The dataset is described in detail by Wentz (1998). In addition to the TMI dataset, and partly to test results from TMI, we used version-5 of the SST data available from the Advanced Microwave Scanning Radiometer-EOS (AMSR-E, Kawanishi et al., 2003) on board of the EOS-Aqua satellite.
We are interested in the question whether Saharan dust (outbreaks and/or seasonal cycle) and its associated cooling can lead to cold SST anomalies in the eastern North Atlantic and to what extent they can be detected in existing satellite SST datasets. To answer both questions one needs a reliable satellite SST database that is not affected in its retrieval procedure by the dust. This holds for microwave SST observations and what follows is therefore mostly based on the TMI SST dataset. Stammer et al. (2003) tested the quality of TMI data by comparing them against in situ measurements on a global scale and found a standard deviation difference of about 0.45◦ C.
To obtain further confidence of the quality of the TMI SST fields, we show in Fig. 2.3a a comparison between SST anomalies as inferred from the TMI (red) and AMSR-E (black) microwave radiometers for the period 2002-2005 averaged over the region (18◦ W
- 25◦ W; 15◦ N - 22◦ N). In both cases the SST anomalies were calculated with respect to a climatological seasonal cycle computed from 9 years (1998-2006) of TMI data. The MW SST anomalies are about the same albeit somewhat smaller in amplitude for AMSR-E. Arrows in the figure mark seasonally high dust loads (in summer, purple arrows) and the strongest dust events in winter (black arrows), as identified from the AOD time series.
A first visual comparison reveals that both MW SST time series decrease simultaneously to most of those events, as it would result from cooling.
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Figure 2.3: (a) Time series of SST anomalies obtained from the TMI (red), AMSR-E (black), and AVHRR (blue) sensors, for the period 2002-2005. In all cases, the SST anomalies were calculated relative to a climatological seasonal cycle computed from TMI data over the 9-year period 1998-2006, and averaged subsequently over 25◦ W - 18◦ W; 15◦ N - 22◦ N. (b) Differences between TMI and AMSR-E data (black) and between TMI and AVHRR data (blue). Also shown (in green) is the time series of weekly averaged MODIS AOD data representing the same area and including the seasonal cycle. Red ar- rows in both panels indicate seasonal high dust loads (centered in July 15, in purple) and black arrows indicate strong dust events in winter (larger than 0.8 for weekly averages, in black).
Also shown in the figure is a time series of SST anomalies from the AVHRR Pathfinder data (Kilpatrick et al., 2001), after subtracting the same TMI climatological seasonal cycle for comparison purposes. Differences between the SST from TMI and AMSRE and from TMI and AVHRR (shown in Fig. 2.3b) indicate that the two MW SST products stay close together (within a 0.5◦ C range; rms(TMI-AMSRE)=0.17◦ C). In contrast, the AVHRR SST estimates deviate substantially from both MW observations (rms(TMI- AVHRR)=0.78◦ C), sometimes by as much as 2◦ C or more during strong dust events, with a clear seasonality also present in the difference. This suggests that AVHRR data is biased cold by as much as 1◦ C or more in this region during summer months.
It is known that both clouds and aerosol can lead to biases between IR and MW SST (Chelton and Wentz, 2005). In our study region, clouds and Saharan dust have both seasonal cycles connected to the seasonal movement of the ITCZ and, in principle, the differences shown in Fig. 2.3 could therefore result from either effect. However, Corlett et al. (2006) previously showed differences between SSTs from the dual view Advanced Along-Track Scanning Radiometer (AATSR) and SSTs from MODIS and AVHRR of about 1◦ C in our study area and argued that they result from dust impact on MODIS and AVHRR retrievals. This conclusion was backed up by Vázquez-Cuervo et al. (2004) who demonstrated that AATSR is less sensitive to aerosols due to the dual view. They also report negative correlations between aerosols and AATSR SST minus AVHRR SST (as well as with in-situ comparisons) in our studied region.
Those earlier results suggested to compare the SST differences shown in Fig. 2.3 with the weekly averaged AOD (Fig. 2.3b). A visual inspection shows a clear relationship between periods of enhanced AOD and associated dust concentrations and periods of large TMI minus AVHRR SST differences, suggesting that the impact of dust clouds on the AVHRR retrieval is the primary agent for causing the AVHRR SST to be biased cold. This applies for dust content on a seasonal cycle as well as for strong dust outbreaks on time scales of up to a few days. These effects are consistent with the earlier findings from Vázquez-Cuervo et al. (2004) and are therefore the consequence of the AVHRR atmospheric correction algorithm failing to adequately compensate for the dust and the dry SAL. We conclude therefore that AVHRR datasets are not appropriate for the study intended here. At the same time it is obvious that microwave SST data have an important role to play in such studies of climate change, especially if there is an expected changing dust load of the atmosphere in response to a changing climate (see Mahowald and Luo, 2003).
2.3 Aerosol Radiative Forcing during AEROSE-I
To understand the impact of Saharan mineral dust on SST of the eastern Atlantic, an important quantity to know is the shortwave (SW) radiative forcing anomaly at sea level associated with a specific dust load of the atmosphere, referred to below as aerosol radiative forcing anomaly flux (ARF in W m−2 ). ARF associated with dust in the SAL is usually computed from AOD fields according to:
ARF = fe · AOD (2.1)
where fe is the aerosol surface forcing efficiency coefficient (in units of Wm−2 AOD−1, see Ramanathan et al., 2001) and AOD is the aerosol optical depth from MODIS discussed above. A few estimates of feare available (Li et al., 2004; Yoon et al., 2005; Zhu et al., 2007).
Fig. 2.4, provides an example of an ARF field that resulted from the March 2004 dust event shown in Fig. 2.1.
In order to estimate the ARF, forcing efficiencies for that month, year and region are needed. Yoon et al. (2005) provide monthly values of fe obtained from observations during the period October 1994 - December 2003. Even though the year 2004 is not
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Figure 2.4: Aerosol-induced Shortwave Radiation Forcing anomaly at sea level, inferred from MODIS-AOD field for March 4, 2004 and results from Li et al. (2004) and Yoon et al. (2005).
included, their results are based on a 9-year climatology, so it seems quite reasonable to use their estimation for March 2004. But, the region for which these results are valid (called Cape Verde in their manuscript) includes a large portion of the African continent (see brown box on Fig. 2.5, left panel) which will lead to misleading results when applying for the oceanic region that is being investigated in this thesis.
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Figure 2.5: (right) Areas for which Liet al. (2004) and Yoon et al. (2005) calculated their fe are shown in blue and brown respectively. (right) Time series of fe extrapolated into the present studied region.
The surface fe obtained by Li et al. (2004), was calculated for a region over the Atlantic Ocean near the African coast (blue box shown on the Fig. 2.5 map), but only values for the high-dust season (June/July/August) and the low-dust season (November/December/January) were provided.
These two results are then combined to obtain monthly surface fe values on the oceanic region that is of interest of this work. The results are shown on the right panel of Fig. 2.5. Using the corresponding forcing efficiency value for March (fe = 80 Wm−2 /AOD), associated ARF amplitudes of up to -300 Wm−2 can be inferred from the MODIS AOD data in some regions during that day (Fig. 2.4). However, a detailed knowledge of fe on this region is missing and it is part of this study to revisit the question of what is the actual amplitude of fe and what its wavelength sensitivity is. With this purpose, data available from the AEROSE expedition will be used.
The AEROSE project consisted of a series of intensive field experiments conducted aboard the U.S. National Oceanic and Atmospheric Administration (NOAA) research vessel, the Ronald H. Brown (Nalli et al., 2005, 2006; Morris et al., 2006; Hawkins et al., 2007). The present analysis is based on data obtained during the first cruise (AEROSE-
I) which took place during spring of 2004, departing from Bridgetown, Barbados, on February 29 and returning to San Juan, Puerto Rico on March 26, 2004, after crossing the Atlantic twice in zonal direction (see left panel Fig. 2.6). During the cruise, the ship encountered two significant Saharan dust events off the African coast in the period 9-18 March underneath which radiometric and ocean observations were obtained (Fig. 2.6, right panel). The column-integrated optical depth observations were obtained by two up-ward looking, handheld commercial Microtops sunphotometers in five different bands and AOD estimates were derived from these measurements according to Knobelspiesse et al. (2004). The concept of Microtops sunphotometer is rather simple. UTC time and GPS location determine how much solar energy can be expected. The measured sun-light provides information, by how much the aerosol has attenuated the direct sun-light. This sun-light sampling is done at specific solar sub-spectral regions to avoid interference by trace-gas absorption. The challenge in operating the instrument is to find cloud (and specially cirrus) free views of the sun and to point the instrument during sampling directly into the sun, with the help of a visual device on top of the instrument.
illustration not visible in this excerpt
Figure 2.6: Ship track and positions of CTD stations conducted during the 2004 AEROSE-I cruise from 9 to 18 March, for the complete cruise (left) and for our studied region (right). Black dots indicate the location where AOD measurements were performed on board the ship several times per day.
In Fig. 2.7 we show respective AOD measurements taken at sea level at wavelengths of 380 nm and 870 nm (Fig. 2.7a, see Fig. 2.6 for locations). Also shown in the figure are SW radiation fluxes measured quasi-continuously at sea leavel (QSL, Fig. 2.7b) from aboard the ship. Apparent from both panels is the impact of clouds on the measurements, especially after March 11. In the solar SW radiation measurements, clouds usually
lead to reduced radiation fluxes; however, in some instances, surface SW fluxes are also enhanced due to forward scattering from the broken clouds when the cloud fraction is small and the sun is in a cloud-free sky (e.g., Pfister et al., 2003). The baselines of the AOD measurements are indicative of dust concentration changes under cloud- free conditions (Fig. 2.7c). Cloud impacts lead to significant variability in the AOD observations. Because the ARF is defined as the difference between the incident radiative flux calculated under clear-sky conditions with and without aerosols (Won et al., 2004; Yoon et al., 2005), we have to eliminate the effect of cloud contamination on the radiation measurements, before fe and ARF can be estimated from the AEROSE-I data.
illustration not visible in this excerpt
Figure 2.7: (a) AOD measurements at 380 nm (red) and 870 nm (blue) and (b) short- wave radiation fluxes, QSL, measured at sea level during the AEROSE-I cruise from 9 to 18 March, 2004 (see Fig. 2.6 for locations). In the bottom row the same two fields are shown after eliminating the effects of clouds. Panel (c) shows cloud-free AOD mea- surements at 380 nm (red) and 870 nm (blue) at sea level, and panel (d) the time series of QSL for clear sky conditions (in blue) superimposed to the cloud-contaminated values (in red; see also text for details).
To identify cloud-free conditions, we use the amplitudes of the normalized short wave atmospheric transmissivity, τ , which is the fraction of incident solar energy incident at the top of atmosphere (TOA, QTOA) that would reach the surface with the sun overhead, and defined as Eq. 2.2 (Fig. 2.8a). Low values of τ result from the presence of clouds,16 Chapter 2 Remote Sensing: SST, AOD. KPP-1D. MITgcm
and anomalously high values occur when the sensor is in the direct beam of the sunlight with additional energy scattered by the clouds.
QSL = QTOA × τ1 /cos(solarzenithangle)
To eliminate cloud-contaminated data, the first step was to discard all measurements for which τ is higher than 0.85 and lower than 0.75 (Fig. 2.8d and 2.8e). The high threshold was chosen to be somewhat lower than the clear-sky normalized atmospheric transmissivity measured in the clear polar atmospheres (Minnett, 1999; Hanafin and Minnett, 2001; Key and Minnett, 2006), and cases with values below the lower threshold were clearly influenced by the presence of clouds.
illustration not visible in this excerpt
Figure 2.8: Measured and estimated parameters from AEROSE-I used to calculate the forcing efficiency fe.
A ’cleaner’ QSL signal is already visible from the Fig. 2.8f (plotted in blue). As a second step of the cloud detection and elimination process, we fitted a sinusoidal function to the resulting SW radiation (Fig. 2.7d) Because March 11 was essentially cloud-free, we used the radiation profile from that day to simulate the cloud-free daily cycle in solar radiation during the following days. But because AOD is varying with time, the cloud-free noon radiation also varies from day to day. To account for this we used a scaled version of the daily radiation cycle from March 11 and superimposed on it the measured shortwave radiation data of all other days.
An estimate of the efficiency factor, fe, was obtained from the differences between the QSL and the shortwave fluxes at TOA (QTOA). These are plotted in Fig. 2.9 as a function of AOD at 380 nm and 870 nm, considering all cloud-free values from 9 to 18 March 2004 and only the AEROSE-I AOD measurements between 0.1 and 0.75 (see Fig. 2.7c). Values of QTOA were calculated for the position of the sun at the location of the ship at the times of the measurements using the equations given in the Astronomical Almanac (Astronomical Applications Department, 1990) and for the refraction of the atmosphere as given by Zimmerman (1981). Using the results from the 380 nm channel, a linear regression between QSL-QTOA and AOD leads to values of fe of:
fe = (QSL − QTOA)/AOD = −73.5 ± 7.1 Wm−2 AOD−1 (2.3)
with a correlation coefficient of -0.41. The slope is smaller (−57.9 ± 8.9 Wm−2 AOD−1 ) when using the 870 nm channel (correlation of -0.27) and using an average of both channels would result in a value of fe = −69.1 ± 8.0 Wm−2 /AOD. We note, for a later interpretation, that the AOD measurements were taken between 13h and 19h local time, and that the fe estimate therefore corresponds to the afternoon situation, rather than to a daily mean field. Compared to previous estimates available from Li et al. (2004), Yoon et al. (2005) and Zhu et al. (2007) (fe ≈ 80W m−2 AOD−1, during winter), our results are somewhat lower, although still close. Considering the offset for AOD = 0 as a further consistency check, the estimates lead to values of -212.2 ± 3.6 Wm−2 and -225.3 ± 3.6 W m−2, for 380 and 870 nm, respectively. In comparison, the theoretical value is
-180 W m−2, which exists for the global ocean. Our estimates are larger, and this can partially be related to regional variations.
illustration not visible in this excerpt
Figure 2.9: Difference between QSL and QTOA for ’cloud-free’ conditions plotted as a function of AOD 380 nm (a) and 870 nm (b). The slope of a least-squares fitted line represents the value of the fe in units of W m−2 AOD−1 (Eq. 2.3).
2.4 Observed SST and AOD anomalies
Examples of weekly-averaged AOD time series during strong dust events and contempo- raneous weekly-averaged TMI SST anomalies (relative to a climatological seasonal cycle), are provided in Fig. 2.10 for the years 2002 to 2005, both averaged over the region 27◦ W - 21◦ W, 19◦ N -26.5◦ N. The figure reveals several intense dust periods lasting several days. It appears that during or after some of those dust events, the SST shows downward tendencies (either as cooling or as reduced warming) as would be consistent with dust-related cooling.
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Figure 2.10: Time series of weekly anomalies of MODIS AOD (triangles) and of TMI SST (stars), averaged over 27◦ W - 21◦ W; 19◦ N - 26.5◦ N, for the periods: April - August 2002 (a) and January - May for years 2003 (b), 2004 (c) and 2005 (d).
Fig. 2.10a reveals an intense dust period during late April and beginning of May 2002. A second (although weaker) dust event occurs in the July/August time frame. After the first dust period, SST declines over a one and a half months period by as much as 1◦ C. The SST subsequently recovers until the end of June, however, consistent with the second dust period, the SST declines again during late July. Similarly, a drop in SST up to about 1.4◦ C is observed in mid-February 2003 (Fig. 2.10b), after one strong dust event occurs in the preceding weeks. SST starts increasing during a subsequent low dust period but shows a new drop after a further strong event at the beginning of March. During 2004 (Fig. 2.10c) two high AOD events occurred in March. Even though this seems to be a period with background positive SST anomalies, the strong dust event in March 4 clearly coincides with a reduction in SST. Finally in 2005 (Fig. 2.10d) the situation is somewhat different in that two dust outbreaks can be observed only at the beginning and at the end of the January-May period (both accompanied by a downward tendency of the SST), while in the rest of the period SST shows strong intermittent SST variability seemingly unrelated to dust outbreaks. So, from a visual inspection of Fig. 2.10 one can hypothesize that during several instances a plausible relation exists between enhanced atmospheric dust loads, associated attenuation of solar irradiance and resulting cooling (or reduced warming) of SST.
Assuming for the moment that any observed change in SST is related to a dust-induced variation in surface heat flux forcing, according to a simple bulk mixed layer relation, given as
illustration not visible in this excerpt
we should be able to find a relation between changes in AOD and tendencies in SST. In Eq. 2.4, ARF(t) could be taken from Eq. 2.1, ρ is a typical density of the upper ocean, cp is the specific heat of seawater and h would be a typical, but known, mixed layer depth (MLD). If, for simplicity, we take the MLD and the fe to be constant with time, then we should expect a linear relationship between the accumulated AOD and the SST. This is consistent with the scatter plot between the weekly anomalies of SST observations and the accumulated AOD for the entire period 2000-2006 (Fig. 2.11), which shows positive (negative) values of accumulated AOD anomalies to be associated with negative (positive) anomalies of SST. The coefficient of correlation (r) is significant at 95% of confidence level and was found to be maximum (r = 0.55) when the anomalies of AOD lead those of SST by 1 week. The slope of the linear regression (-0.27◦ C AOD−1 ) leads to an estimate of the mean value for the mixed layer depth of about 22m. This is somehow shallower than those values of de Boyer Mont é gut et al. (2004) and our findings in the next section. Nevertheless, the value is plausible and supports the validity of a relation between SST trends and AOD.
illustration not visible in this excerpt
Figure 2.11: Scatter plot between accumulated weekly anomalies of MODIS AOD and weekly anomalies of TMI SST, for the region 27◦ W - 21◦ W; 19◦ N - 26.5◦ N and for the period 2000-2006. The AOD is leading the SST for 1 week. The red line represents the fitted least-squares linear regression. The resulting coefficient of correlation and slope are 0.55 and -0.27, respectively.
The results shown in Fig. 2.11 suggest that about 30% (i.e.: r2 ) of the SST variance could be explained by those of the accumulated AOD in our study region. However, the remaining 70% of SST variance occur on all time scales because many processes lead to SST changes, most of which are not related to dust events at all. Accordingly, dust- induced SST anomalies will always be superimposed, or even masked, by SST changes associated with ocean dynamics or remote forcing. Separating local dust effects from dy- namical SST variations (e.g., resulting from mechanical-wind stirring, upwelling and/or eddies and planetary waves) remains a challenge in any study based on (satellite) data alone, implying that more information from ocean dynamics is needed in any quantitative investigation.
We conclude that a quantitative and unambiguous connection between Saharan dust outbreaks and surface cooling as hypothesized by Miller and Tegen (1999) cannot be made convincingly from the data at hand, but that additional information is necessary, e.g., as available from ocean dynamics embedded in circulation models. Nevertheless, a significant relation between SST changes and dust appears to be present.
2.5 Simulated SST anomalies in the ocean mixed layer
To simulate the response of SST to dust-induced cooling, an approach based on a simple bulk mixed layer model would be an oversimplification, since the MLD, taken to be constant and known in Eq. 2.4, in reality is highly variable in space and time due to its dependence on many parameters, including surface wind stress. To further aid the investigation of dust effects on SST we use here a local mixed layer model to determine the amplitudes of SST anomalies that can be expected during individual dust events. In the next section, the use of a three-dimensional circulation model will help to identify dynamical SST features.
The state-of-art 1-D mixed layer model of the upper ocean is based on the coupled KPP mixed layer model (Large et al., 1994) (the model will be referred to as KPP-1D henceforth). The philosophy of this conceptual study is to neglect advective processes and thereby to investigate the magnitude of SST anomalies that can be forced locally by strong dust events.
Two distinct vertical mixing schemes in the oean are considered: mixing in the ocean’s surface boundary layer (OBL) and in the ocean’s interior.
Mixing in the OBL near the surface happens under various surface forcing conditions (buoyancy and momentum). It consists of the 1-D upper ocean mixing parameterization in which a bulk Richardson number is used to determine the depth of the OBL (h), and a non-local KPP is applied subsequently as the vertical mixing scheme in the OBL.
The expression for the vertical turbulent fluxes of momentum wx and tracer properties
illustration not visible in this excerpt
where d is the distance from the boundary, and d = −z in the OBL. It consists on the sum of a down-gradient flux (∂X/∂z) and a non-local transport term (γx) that enhances the gradient-flux mixing coefficient (Kx) further where the water column is unstable. In other words, it has a diffusivity component and a non-local transport component. The model works as follows: the external forcing is prescribed, h is determined and the difussivity and non-local transport profiles are computed. The profile of the diffusivity is defined as follows:
illustration not visible in this excerpt
where wx is a depth dependent turbulent velocity scale, G(σ) is non-dimensional vertical shape function1, and σ = d/h is a dimensionless vertical coordinate. The non-local transport term (γx) is non-zero for scalars in convective forcing conditions (i.e., salt and temperature, see Large et al. (1994)).
In the interior, mixing is due to internal wave activity, shear instability (dependent on a local gradient Richardson number2 ), and double diffusion (molecular). Eq. 2.6 is matched (itself and the first derivate) to the interior, and γx = 0.
In the runs performed, the vertical resolution is 1 m over the top 100 m. To run the KPP-1D model, initial temperature and salinity profiles were used as provided by CTD profiles collected during AEROSE-I at the location 19.0◦ W, 18.0◦ N (Station 5 in Fig. 2.6).
To simulate the effect of Saharan dust cooling of the sea surface, two simulations were performed: a control run and a perturbed run. The control run was driven by net forcing fields provided every 6 hours by the National Center for Environmental Predic- tion/National Center for Atmospheric Research (NCEP/NCAR) Reanalysis-1 (Kalnay et al., 1996). This version of the KPP-1D model can be forced either with the state of the atmosphere, or directly with the fluxes. In this case, we prescribed NCEP reanal- ysis surface fluxes which included wind stress, sensible heat flux, evaporation, radiative fluxes and precipitation. The evaporation was estimated with the latent heat fluxes from NCEP/NCAR Reanalysis-1 and the enthalpy of vaporization. Fields were linearly interpolated every 30 min. from the available 6-hourly values. Because the NCEP forc- ing does not include any impact of Saharan dust on the surface SW forcing (Lacis and Hansen, 1974), this run is not affected by any dust-related cooling. The perturbed run incorporated the dust effect inferred from the MODIS-based AOD time series as shown below.
The effect of dust loads was incorporated into the model through a reduction of the NCEP SW forcing by the ARF forcing. To this end, the following steps were performed:
1. The MODIS daily AOD time series was evaluated at the station location and converted into daily ARF according to Eq. 2.1, with fe values provided by Eq. 2.3.
2. In a second step a modified SW forcing was constructed that included the effect of Saharan dust according to:
SW (t) = SW (t)(1 − ARF/SWmax),
where ARF was provided every day, SW(t) was available every 6h and SWmax is the maximum noon radiation value. In this way, the night values are not altered and a maximum reduction of the SW is obtained at noon of every day.
3. No other dust effect on the surface radiative forcing was accounted for, such as enhanced incident longwave radiation. This step is justified by Vogelmann et al.
(2003), who showed that the respective forcing would only be of the order of ±10W m−2 which can be confidently neglected here.
The decrease in surface temperature resulting from the difference between the per- turbed and unperturbed runs is therefore due only to the SW flux anomalies derived from the presence of dust in the atmosphere. Because what matters to our analysis here is the resulting ocean temperature at the uppermost level of the model, in the following we will only show the top level temperature anomaly, assuming it is equivalent to the SST anomaly. Results are shown in Fig. 2.12, for strong dust outbreak periods during winter 2003 and 2004. Shown in the top row of the figure are SST anomalies as they result for the periods February 1 through March 31, 2003 (left) and February 1 through March 31, 2004 (right) with a temporal resolution of 30 min. Also shown are MODIS daily AOD observations at the same position. Because in our study dust impacts only the SW solar irradiance, SST anomalies show a clear daily cycle with maximum negative amplitudes occurring during mid-day and close to zero changes during night time. Moreover, an overall decrease due to the general presence of dust during the entire considered period is observed.
Focusing first on the left panel, two dust events are apparent from the AOD time series during early 2003, with peak AOD values of about 1.9 occurring during February 11. A second and somewhat longer event was observed since the beginning of March (0.7 < AOD < 1.7). In both cases, SST decreases are simulated during and shortly after peak dust concentrations. This is specially obvious during the second event lasting for about 5 days in early March, when SST decreases by about 0.3◦ C. Even though a quantitative connection was not possible from our analysis of Fig. 2.10, the decrease observed at the beginning of March 2003 (Fig. 2.10b) agrees with the magnitude simulated here. We note that only weekly averages were shown in Fig. 2.10, which inevitably lead to smaller amplitudes in the SST anomaly and temporal shifts of the maximum response. We also note that the first dust event, ocurring on February 11, has a smaller signature in SST, yet the forcing amplitude appears larger compared to the March event.
To understand why this is so we show, in the middle row of Fig. 2.12, anomalies of the SW forcing together with the absolute value of wind forcing. Moreover, shown in the bottom row of the figure are time series of the SST and MLD for the perturbed and unperturbed runs. The MLD is fairly deep during the beginning of February (around 40 m). A decline of MLD occurs during early March, when the wind stress suddenly drops to a minimum, leading to a MLD of less than 15 m. The same holds during 2004 (right column): a shallow MLD is present only at the end of March (neglecting the two intermittent shoaling events), while the major dust event occurred 20 days before. Accordingly, the SST response simulated during 2004 is likewise moderate and only of the order of 0.1◦ C.
The experiments suggest that, if applied only over short periods, dust-induced cooling of the surface strongly depends on the structure of the upper ocean and especially the thickness of the surface mixed layer. To have a measurable impact on SST, a shallow mixed layer is required simultaneously to enhanced dust loads. Wind stirring tends to deepen the mixed layer through mixing and would thereby eliminate the signal. Am- plitudes of SST anomalies, simulated with the KPP-1D model, are comparable to those observed in Fig. 2.10 shortly after strong dust events. However, while observed changes
illustration not visible in this excerpt
Figure 2.12: Results from the KPP-1D simulations for the years 2003 (left column) and 2004 (right column) at the position of CTD Station 5 (19◦ W, 18◦ N, see Fig. 2.6). Top row: Daily MODIS AOD (blue) plotted together with the 30 min. SST difference between perturbed and unperturbed runs (black). Middle row: ARF (blue) and wind stress magnitude (red). The wind forcing was the same for perturbed and unperturbed runs, and the heat flux shown is the difference between the forcing for the perturbed runs and the forcing for the unperturbed runs, i.e., the anomaly associated to ARF. Bottom row: Daily SST (black) and mixed layer depth (blue) for the perturbed and unperturbed runs. Solid and dashed lines in the bottom row panels represent unperturbed and dust- perturbed runs, respectively.
are plausible, both in terms of amplitude and phase, a definitive proof of them being generated by dust cannot be given from the 1D simulation; instead a full ocean circu- lation model is needed (next section). Nevertheless, the results provide the important information that a strong response of SST due to Saharan dust can be expected only during periods of low wind stirring (and associated low mixed layer depth) and that therefore more emphasis needs to be put on the impact of dust on SST on the seasonal time scale, discussed in the next section.
[...]
1 http://jwocky.gsfc.nasa.gov/aerosols/africa/canary.html
2 http://gdata1.sci.gsfc.nasa.gov/daac-bin/G3/gui.cgi?instance_id=MODIS_DAILY_L3
1 See Fig. 2 from Large et al. (1994) for examples of G(σ) and wx(σ) profiles.
2 The gradient Richardson number is defined as: Ri(z) = N2 (z)/(dU/dz)2. See Kundu (1990).
- Quote paper
- Nidia Martínez Avellaneda (Author), 2010, The Impact of Saharan Dust on the North Atlantic Circulation, Munich, GRIN Verlag, https://www.grin.com/document/146039
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