4. Development of the Mediterranean box model
4.3. Model development
To quantitatively investigate the Mediterranean planktic foraminiferal δ18O signal for sapropel S5, I further develop the Mediterranean box model to run as a time series through S5, constrained by proxy records for sea level and sea surface temperature (SST). In this chapter, monsoonal runoff parameters are adjusted for specific intervals through the S5 interval, and the model then gives the expected foraminiferal δ18O for the different Mediterranean surface and intermediate water masses, for comparison with the multi- species δ18O dataset that I compiled for S5 (Chapter 3).
The model developed here builds on the most recent version of the Mediterranean box model (Rohling et al., 2014). However, given that the main interest here concerns sapropel events, the monsoon box of the Rohling et al. (2004) model has been reinstated. Both of the previous model versions were presented as Mathcad scripts. Therefore, in order to increase accessibility to the model, the first task was to translate the Rohling et al. (2014) Mathcad script into the more widely used MATLAB notation (Appendix A5). All subsequent model development, including adding the monsoon box of the Rohling et al. (2004) model and the model adaptions described below, continued in MATLAB. The final model developed and used in this chapter is included in Appendix A6.
4.3.1. Running the model for a time series
The model outputs are going to be compared with the eastern Mediterranean S5 δ18O dataset (Chapter 3; Fig. 3.5), which is already on a single, common, stratigraphically correlated depth scale (ODP 971A-equivalent depth, see section 3.3.3). At this stage, the depth scale will continue to be used to describe the progression through the study interval. The model was run as a series of progressive 0.1 cm (ODP 971A-equivalent depth) steps. A 0.1 cm depth step is equivalent to approximately 30 years during S5 deposition, which is roughly 3× longer than the residence times for both surface waters and intermediate waters during sapropel intervals (~9 and 13 years respectively, as calculated by the
model). Hence, I assume that for each depth step at which the model is run, the different water masses in the basin reach a steady state. At each step the model iterates 30 times, which corresponds to the average number of annual cycles in a depth step.
4.3.2. Using proxy records as inputs
To run the model for a specific time interval, it needs to be considered that some parameters set in the model will change through time. The three most important time- dependent parameters, especially for investigating δ18O, are sea level (a proxy for global ice volume), sea surface temperature (SST), and excess freshwater inputs (during sapropel events).
Previously, the model was run individually for a series of different sea-levels, with SST in the model set to vary linearly with sea level (Rohling et al., 2014). However, for the time interval of sapropel S5, independent proxy datasets exist for sea level and Mediterranean SST. In the new model, these proxy records are used to directly constrain sea level and SST, enabling the model to be run specifically for the case study interval of sapropel S5. Additionally, the independent forcing of sea level and SST reduces assumptions made of co-variation between temperature and sea level, which is important for accurately defining the influence of these two components on δ18O.
The Red Sea sea-level record of Grant et al. (2012) is used to force sea level in the box model. It is a continuous, highly resolved, and independently dated (i.e., radiometrically assessed) record that covers sapropel S5. The results of the probabilistic assessment of the Red Sea sea-level record were transferred onto an ODP 971A-equivalent depth scale using the LC21 age model of Grant et al. (2012) and the stratigraphic correlation between LC21 and ODP 971A of Marino et al. (2007).
For SST, I use records based on the alkenone unsaturation index (UK’37) and carbonate clumped isotope thermometry (Δ47) from the eastern Mediterranean (Rohling et al., 2002; Marino et al., 2007; Rodríguez-Sanz et al., 2017). SST records derived from both methods are used as inputs for the Mediterranean box model in this study (see section 4.4.1). UK’37-based SST reconstructions exist for the S5 interval at all four of the eastern Mediterranean sites included in this study (Rohling et al., 2002, 2004; Marino et al., 2007). Each SST record was transferred onto the ODP 971A-equivalent depth scale as described
in section 3.3.3. An eastern Mediterranean stack of the four records was created using a Monte Carlo simulation which was run 10,000 times, each time sampling the data points from all four cores from within their uncertainties. The resultant outputs from the simulation were used to calculate the 2.5th, 16th, 50th, 84th and 97.5th percentiles of the probability distribution. From this I obtained the median, along with 68% (16th - 84th percentile) and 95% (2.5th – 97.5th percentile) uncertainty envelopes of the stack, which were then smoothed using a Gaussian filter with a depth window of 1 cm. This eastern Mediterranean UK’37-based SST stack was taken as an approximation of annual average SST for the eastern basin (Rohling et al., 2002), with a seasonal deviation of +/- 3°C applied for summer/winter SST when applied in the model (Stanev et al., 1989). Δ47- based SST records have been constructed using G. ruber (w) for sites LC21 and ODP 967 over the S5 time interval (Rodríguez-Sanz et al., 2017). A subsequent Δ47-based SST eastern Mediterranean stack has been created from the two individual records using the same method as described for the UK’37-based SST stack above. The G. ruber (w) Δ47 is a specific record of temperature for G. ruber (w)’s habitat, i.e., the summer mixed layer
or freshwater lenses during the monsoon season (Emeis et al., 2003; Rohling et al., 2004; Rodríguez-Sanz et al., 2017). Uncertainties in the temperature and sea-level records, along with those of all other input parameters, were included and propagated through the model (see section 4.3.4).
4.3.3. African monsoonal freshwater runoff
The other important time-dependent parameter to be defined for the model is excess freshwater input to the eastern basin during the sapropel S5 event. The spatial gradients in S5 eastern Mediterranean planktic foraminiferal δ18O (Chapter 3; Cane et al., 2002; Marino et al., 2007) and neodymium isotopic composition (εNd) data (Osborne et al., 2008, 2010), indicate that the African continent was the predominant source of excess freshwater input to the basin, and that freshwater contributions from the European borderlands were negligible. Therefore, I assume in the model that all excess freshwater input to the Mediterranean during S5 deposition is African freshwater runoff.
The Mediterranean model represents the changed basin conditions during sapropels using a two-month ‘monsoon season’ (Fig. 4.1). Here, the monsoon box allows excess monsoonal freshwater associated with sapropel events to be input to the surface waters of
the model. This allows for the fresher, more buoyant waters to remain, more realistically, at the top of the water column during the monsoon season, instead of being immediately mixed throughout the full depth of the summer mixed layer. The depth of this freshwater- diluted ‘upper summer mixed layer’ is represented by the depth of the monsoon box in the model, and is initially set to a basin-mean value of 5m, following Rohling et al. (2004).
The study interval also encompasses time before and after sapropel S5, when there is no evidence of excess freshwater input from an enhanced African monsoon. Additionally, there is a sapropel ‘interruption’ in S5, where excess freshwater influx is thought to have diminished, if not completely ceased (Cane et al., 2002; Rohling et al., 2002, 2004; Scrivner et al., 2004). To model both ‘sapropel-forming’ conditions and ‘normal’ conditions, different stages were defined within the study interval (Table 4.1). These stages were identified by the visible sapropel layers in the sediment cores and features observed in the δ18O dataset (section 3.4). The different stages were set to have the excess monsoonal freshwater input switched to either an ‘on’ or ‘off’ mode. In the ‘on’ mode, excess freshwater runoff is input to the monsoon box which represents the freshwater- diluted upper summer mixed layer. The excess freshwater runoff volume is defined as a runoff intensification factor relative to the ‘normal’ present-day (pre-Aswan damming) total runoff input volume (0.45 x 1012 m3 yr-1, Carter, 1956; Schink, 1967; Garrett et al., 1993; Rohling et al., 2004).In the ‘off’ mode, the excess freshwater runoff input is set to 0, and the 'monsoon box' is switched off.
Both the volume and δ18O of African monsoonal freshwater runoff into the Mediterranean during the deposition of sapropel S5 have not yet been fully quantified. However, Rohling
et al. (2004) provided estimates of the volume of monsoonal freshwater runoff for S5, suggesting increases in runoff of 160-300% during the earlier (‘lower’) lobe of S5, and of 120-200% during the later (‘upper’) lobe. Additionally, several studies (Thorweihe et al., 1990; McKenzie, 1993; Hoelzmann et al., 2000; Rodrigues et al., 2000; Beuning et al., 2002; Al Faitouri and Sanford, 2015) indicate that the monsoonal freshwater that affected regions of North African that are today covered by the Saharan desert, was isotopically very light, with δ18O (SMOW) between ~ -8 and -12 ‰. These estimates are used as initial constraints to monsoonal runoff volume and it's δ18O. The model accounts for the ranges of estimates in the same way that uncertainties are accounted for with other
input parameters. The monsoonal parameters are defined as a median value with a 2- standard deviation range corresponding to the known range of possible values for the parameter in question (see Table 4.1).
Table 4.1: Different stages in the study interval and the associated monsoonal parameters in the model. Interval Depth
(971A equivalent, cm)
Excess monsoonal freshwater input
On/Off
Monsoonal runoff parameters Volume δ18O
Pre-sapropel > 62.5 Off 0 N/a
S5 lower lobe 56 – 62.5 On 1.6 - 3 x
present day -8 to -12 ‰
Sapropel
interruption 52 – 56 Off 0 N/a
S5 upper lobe 41 – 52 On 1.2 – 2 x
Present day
-8 to -12 ‰
Post-sapropel < 41 Off 0 N/a
4.3.4. Uncertainty propagation
Each input and parameter within the model has an associated uncertainty, or in the case of the monsoonal parameters a range of possible values. These are defined in the model as probability distribution functions. To fully account for these uncertainties, they need to be propagated through the model. This was done using a Monte Carlo-style approach to run the model 10,000 times, each time sampling the different parameters from within their uncertainties. The resultant 10,000 model outputs from all the model runs were then used to calculate the 2.5th, 16th, 50th, 84th and 97.5th percentiles of the probability distributions for each output parameter. This enabled the median and 68% (16th - 84th percentile) and 95% (2.5th – 97.5th percentile) probability envelopes of all the calculated output parameters to be defined.