Francesca had been coming and going all over the place. One day it had been taking bulbs out of cold stores, the next it had been sowing seeds into pots. No sooner had she got the hang of one job than Simon sent her off on another. It was interesting and exciting but she felt she was being filled up with gardening knowledge as fast as the Gardeners could pour it into her and wondered if she might overflow at any moment. Even now, though it was the end of the day, she had one last errand to run.
The Glasshouses not only supplied culinary herbs for the Kitchen but also medicinal herbs to the Infirmary. They grew poppies and harvested the sap for the relief of pain, feverfew for lowering the temperature, valerian as a sedative and foxglove for pain of the heart, as well as several other plants for specific medical purposes she didn‘t yet understand. One of the children had been taken to the infirmary last night suffering from a fever. Normally, the sick children stayed in the Crèche. Since this one had been taken to the Infirmary it must mean the case required medical experience beyond that of the Crèche Mothers. Late in the afternoon a message had come from the Infirmary that they need fresh feverfew and valerian. So Francesca had been despatched to gather the required herbs and to take them over urgently.
She had come out from the top end of the Glasshouses and had picked up the track that led back towards the suspension bridge. From this path she could see all the north side of the community. The Gatherer longhouses were on the north side of the Gathering Hall. There were a dozen in all, set around courtyards; each with room for five couples. All the Gatherers lived on the north side; the seven Apprentice roundhouses were on the south side. The Crèche was to the southwest next to the Infirmary. The working areas, Smithy, Pottery, Solar-ovens and Kitchens were to the northwest. Between Hall and river there were no buildings, except the small guardhouse where the path to the suspension bridge cut the protective bank-and-ditch.
Since she was going as fast as she could, she was soon at the top of the stone steps down to the suspension bridge. Near the top was Sylvia, who was having difficulty managing to get down the first few steps due to the stiffness of her joints. Francesca hesitated. Sylvia was very independent and the pain she experienced often made her sharp-tongued. She might not thank Francesca for help down but passing her on the steps without helping was impossible. But the herbs were urgent and if she waited for Sylvia to make it down under her own power it might take some time. Francesca hesitated.
‘Stop farting about, whoever you are; you’ll just have to wait.’ Sylvia had her head down and was prodding at the next step with her staff.
‘But, err, ma’am it’s the herbs.’
Sylvia turned slightly. ‘Oh… Ah… Francesca. Well I suppose you’re right. I shouldn’t get in the way of one of my own on an urgent errand. But the fact is I can’t get back up to clear your path so I’m afraid you’re going to have to help me down if you’re going to get on.’
Francesca gingerly climbed down on to the steps. The herbs were packed in her bag so her hands were free but she didn’t fancy having the responsibility of getting Sylvia down safely. Dropping the Chief Gardener on the steps would be a bad black mark and Francesca was conscious she was still on probation as a Gardener.
After a bit of negotiation Sylvia gave Francesca her staff and put her arm over her shoulders. With Francesca supporting her weight, they went slowly down step at a time. When on the bridge Sylvia was able to pick up her pace and took back her staff.
‘Thank you young woman. If you breathe a word of this to anyone you’ll end up as manure in the borders of the main dome.’
Francesca smiled, ‘Your secret’s safe with me ma’am.’
‘Well you better get along now. Just one thing before you go. I was going to tell you tomorrow but now is as good a time as any. The Council will confirm you as Gatherer at the Harvest Festival as planned. You’ve worked as hard as anyone I can remember to learn everything we’ve been able to show you. You’ll more than do.’
From the Archive of Master Tobias
FE modelling of deep ocean currents by ALMA, Journal of Physical
Oceanography 30, 7, 750-753, 2030
High Density Finite Element Analysis of
Thermohaline Currents in the North Atlantic
L P Troubadour*, T J Smith*, F Ramaux** and A J Benion*1
Abstract
This paper presents a pilot study into the opportunities that the use of Advanced Large Multicore Array (ALMA) computers may offer to higher density modelling of ocean bed currents. The experiments reported used finite element analysis of the thermohaline currents in the North Atlantic with special reference to interaction with North Atlantic Drift. The simulations improved convergence of model by between 100 to 500 times at resolutions 100 times higher than conventional simulations of the same problems. Simulations connected surface current predictions to deep ocean bed currents and suggests that significant localised areas of upwelling and sinkage of water between the surface plane and the ocean bed may be present at the borders of four ocean floor basins east and west of the mid Atlantic Ridge. These findings were consistent for a wide range of boundary conditions used in successive simulations.
Keywords: ALMA, finite element analysis, ocean current modelling, thermohaline currents
Introduction
Recent advances in multithreading approaches to finite element analysis on Advanced Large Multicore Array (ALMA) computers have raised the possibility that high density finite element analysis of ocean current fields could be applied at improved resolution. When combined with details of ocean floor maps from the GOCE Gravity Survey this has made it possible to consider modelling of not only the surface currents and temperatures but also the difficult-to-observe ocean floor currents, offering the possibility of new insights into the details of thermohaline circulations.
This paper reports the results of an initial study using the ALMA at Aberdeen to model the ocean floor current structure of the thermohaline circulation of the North Atlantic.
Method
A triangular finite element grid of 106 points was set up to cover a quadrilateral section of the North Atlantic from 25.6° north, 47.9° west to 94.9° south, 5.5° east.
Initial conditions were obtained from a combination of publicly available data sources [1] and our own research data [2, 3]. Mean gravitational vectors and initial mean water pressure data for each element were calculated using ocean floor height and water column data from the GOCE Gravity survey [4]. Initial salinity and surface sea temperatures were derived from the World Ocean Database [1].
Hagen-Poiseules Equation was then used to calculate the mean flow vector in each of the elements at the surface and at the ocean bed. The Beatty-Smith relaxation algorithm [5] bounded by global limits on groups of functionally related elements were used to resolve any boundary condition conflicts by semi-local smoothing. Convergence of the model was determined by the Whittaker-Green criteria [6].
There were three phases to each stage of full model iteration. After the boundary conditions had been set surface current patterns were partially establish by multiple iteration across the surface field without modification of the ocean floor layer. When interactions of the surface model were broadly stable according to the criteria employed by Ramaux and Smith [7], the surface layer was allowed to interact with a still unmodified ocean floor layer to identify significant points of sinkage of water from the surface to the ocean floor and of upwelling of water from the ocean floor to the surface layer.
In the last phase points of significant upwelling and sinkage were fixed and the ocean floor layer fully connected to the surface layer using them and Gaussian assumptions of diffuse sinkage and upwelling between the fixed points of significant sinkage and upwelling. The fully connected model was run to local convergence before smoothing criteria between cells was applied and a new stage of iteration initiated.
The iteration process was deemed concluded when the mean RMS error from model findings and 100 known data check points acros
s the whole region modeled were below 0.1%.
Results
Full iterations took from 10,000 to 100,000 stages depending on exact boundary conditions. We estimated an improvement in time to convergence of the model using the ALMA of between 100 to 500 times for comparable models run on other machines at resolutions 100 times lower.
While there were differences between details in the different interactions the results they produced were very consistent. These are well represented in Figure 1 which shows the typical results of modelling at the surface (1a) and ocean floor levels (1b).
Figures 1: Typical results results of modelling of currents at the surface (la) and ocean floor levels (1b)
Discussion
Clearly the expectation that the use of ALMA architecture machines in this computer-intensive type of modeling task is justified by the results of this short study. The challenge will now be to improve the design of the mathematical algorithms driving the finite element analysis to exploit this advantage in speed and resolution.
However, it would be remiss of us not to consider the implications of the model results in terms of what they may indicate about the structure of thermohaline circulation in the North Atlantic. The consistency of the models in their predictions, particularly of the ocean floor currents, was unexpected and they challenge several established assumptions.
The first is that even in areas such as the South Atlantic Maelstrom upwelling and sinkage is a broadly diffuse process. Whilst in many ways the model is consistent with this assumption it identifies a set of well focused regions of upwelling and sinkage across the area which if present cannot be accounted for by standard assumptions.
Second, the modelling suggests that there are four defined ocean bed basins which form on the western and eastern upslopes of the mid-Atlantic ridge.
It has been known for some time that the undersea trenches between the Outer Hebrides and the Iceland, and Iceland and Greenland are the main bottlenecks in the return of water from the North Atlantic Drift when it sinks in the area between Norway and the Polar Ice Cap.
Our modeling suggests that the effect of these two trenches combines with the barrier of the mid-Atlantic ridge to partition the feedback of the water from the North Atlantic Drift unevenly between west of the ridge and east of the ridge, approximately in the ratio of 1:2. As the water from the trenches flows down each side of the ridge it settles into the low lying areas off the continental shelf of the Bay of Biscay and the Canary Islands in the east and off Labrador and Florida in the west. The influx of this water displaces the cold water from the ocean floor in these area areas mainly diffusely but on the borders of what we would describe as these functional ocean sea basins, areas of significant upwelling and sinkage arise.
We would hypothesise that these local areas of upwelling and sinkage contribute significantly to the cold surface Canary Current and the cold currents off Labrador and the east coast of the USA.
Conclusion
If the structure of deep ocean basins suggested by our modelling can be confirmed by direct observation then it will radically affect our understanding of the dynamics of North Atlantic Drift. In turn this would have a marked effect on our understanding and predictions about what may happen to weather patterns in the North Atlantic if global warming affects thermohaline circulation by weakening the North Atlantic Drift.
References
World Ocean Database, National Oceanographic Data Centre, www.nodc.noaa.org
Benion, AJ Sinkage and Upwelling in the North Atlantic. Journal of Physical Oceanography 2025; 20(3): 230-245.
Troubadour, LP and Rameaux, F Annual variation in surface temperature at the junction between the Canary Current and the South Atlantic Maelstrom, Limnology and Oceanography 2024; 30(4): 371-387.
GOCE Gravitational Variability Data www.esa.com
Beatty, SF and Smith, PG Relaxation algorithms for current field extrapolation: Smoothing and Relaxation Criteria Ocean and Climate Modeling 2028; 12(3): 120-125.
Whittaker, KL and Green, JW Convergence in large finite element fields, Finite Element Analysis in Hydraulic Engineering 2029; 14(12): 450-461.
Ramaux, F and Smith, T J Mathematical stability in surface reaction fields Mathematical Methods in Physical Oceanography 2029; 13(8); 560-565.
Chapter 6
I had transferred as much of the book store as I could to the boat given that I was going to have to house eleven or so ‘guests’ for the trip. Robert had allowed me to include all the newspapers and magazines but I didn’t take this as a gesture of generosity; on the contrary. The books were merely part of the agreed cover story which was that Robert had done a deal with me of which the city builder stuff from the store was part. After the deal had been announced a rumour had been started that said when I came back I’d bring three other ships with me, all full of food. That kept everyone happy. Ordinary scavengers had started shaking my hand as I passed and suddenly the guards were respectful.
Robert had been careful to keep me away from the Lady, which suited me. I couldn’t make up my mind whether she had been part of an elaborate plot to trap me from the start or whether Robert had simply seen the emotional impact she made on me and played accordingly. On balance I thought it was probably a bit of both. She would have to have played along once Robert had told her to pull me in. I had observed that when up against it human beings had great deal of difficulty in being honourable no matter how good their intentions. That took real determination and strength of character. People in the past had called it moral fibre and I clearly lacked it. I could not let Robert succeed but I had no plan to stop him. I probably didn’t have the courage either. I comforted myself in the fact that that was the journey and the sea was always an unpredictable place.
‘We fit for voyage yen?’ Robert was standing too close to me for comfort, deliberately impressing on me his physical presence. Over his shoulder I could see the Lady at the prow of the boat with a guard. Robert had come on board to check my progress and brought her to remind me of what was at stake.
‘Getting there. How much food you want take up to city to fool people?’ I asked.
‘None.’
‘Surely they fight if see you running?’
‘So what yem do; plenty bullets.’ Not only was Robert prepared to condemn his people to starvation but he was quite prepared to rub their noses in it at the same time. ‘Anyway yem not see us go; me go at night.’
‘Then your men going have to row. Channel too narrow use the sail at night, Need all my time, steer a safe course. Only rowing do.’
‘They learn under your wise instruction.’
‘And me need all light as I can get. When moonfull?’
‘Me think of that; night after next. We’ll go then. Me not as stupid as yen think Ostlander.’ He left my side and wandered forward to the Lady and in full view of me, cupped his hand under her chin, forced her head back and kissed her on the lips.
The anger started in my guts and rose up through my chest. My pulse increased and I knew I was going white. It wasn’t jealousy driving it; it was the realisation of my own foolishness. How, with all my knowledge, all my experience, had I been so easily read and trapped? How? The desire to take the spike I had been using to splice a new rope for the sail, walk over there and thrust it up under Robert’s chin, through his tongue, pallet and the bottom of his brain case, into the soft tissue beyond was almost overwhelming. I was disgusted with myself and what I was going to help him do.
Eventually I persuaded Robert that they should keep up the sham of me coming back by holding a feast. I had told him that the journey to the nearest community, one that was rich and that would be easy to conquer, was no more than three days, so they could afford to cover their departure with a celebration. At midnight, they would accompany me to the boat and hail my departure.
So, I had brought enough food from the boat to make a decent meal, built a fire in the main hall and put the rest of my venison to roast over it on a spit. When the g
uards and the rest of the gang members arrived, two kegs of brandy were opened and tots of the spirit handed round to everyone except those who were to sail with me. The remnant of the hardbread from the boat’s hold was distributed to the ordinary gang members; the venison was kept for the guards.
It was the first time I had seen all the gang together in one place. The whole group did not amount to more than sixty. Robert was right to be keen to go. They were closer to the end than I had anticipated. The social fabric of the gang, such as it was, was about to implode.
I sat between Robert and the Lady. Her touch was painful, made worse by the fact I could not speak to her or exchange glances, since we were under Robert’s eye. At what I estimated to be midnight Robert got up to speak. The hall became quite.
‘Friends. Tonight marks new beginning. The Ostlander has brought us new hope. Tonight he leave. In few week he be back with more food. Friends, I give you Tobias the Ostlander.’ Robert held out his cup and drank; cheering followed from the guards and the rest of the gang. Robert fired his pistol at the ceiling. Like Robert the forty-nine who were to be left behind were drunk; the nine who were coming were sober.
‘Friends let us give yem good send off.’ Leonard and Angus seized hold of me and put me on their shoulders. They carried me out of the hall and into the night followed by all the guards and the cheering people.
The boat had been prepared; even its four oars had been placed ready in the rowports. On the pretext of moving the boat so that it pointed downstream, I had even managed to train a few of the guards to row. We arrived at the gangplank and they put me down. I waved and grinned at the crowd. ‘Thank you friends. When return yen no more hunger.’ Strictly not a lie, I thought, for even if I never came back death would soon come to end their starvation.