Modelling the Monks' Mess Hall (Part 1)

I asked National Weather Service Hydrologist Andy Wood what he would ask people from other countries to understand the role of humans in their process of making river forecasts. He wanted to know how the humans interact with their models. Do the humans do a lot of intervention, adjustment and interpretation (like cooking over a campfire)? Is it more hands-off (like a microwave oven)?

Models come in many forms, but basically they are quantitative summaries of how people believe nature works. They are the vessels that scientists pour their knowledge in to. Models play a central role in nearly all forecasting (and for a good chunk of scientific research as well) so it seems that a discussion of them here is inevitable.

The classic analogy for hydrology models is that soils hold and release water like a series of leaky buckets. But instead, let's start by discussing how to model a cafeteria/mess hall/canteen for hungry meditating monks.

During my 10 days of silent meditation, the meals were a highlight and I looked forward to going to the cafeteria each day. When all you have to do for hours on end is concentrate on the breath whistling past your nostrils, you can entertain yourself by conjuring back-stories for that hairline crack in the wall. Lets just say I had a lot of time to ponder the how the cafeteria worked. I am also convinced that two different people painted the cafeteria's walls, one Swiss, the other a drunk.

A typical lunch at Vipassana. The food was quite good, really. Day 6's tofu dish still gives me cravings and attachment.   

Let us imagine that monks arrive at a building (like precipitation falls on a catchment). They can all arrive at once (a big downpour) or leisurely drizzle in over some period. The monks disappear into the building for a while (like rainfall goes into the soils). Later we see monks leaving the building (much like how water would drain out to a stream). The challenge is that we cannot go inside the building, we can only make a model based on, say, walking around the building (like measuring soil properties) and observing monks going in and out (the equivalent of measuring rainfall and streamflow).

The eating area for females in the meditation center

One cafeteria-ologist standing outside the building could hear the cacophany of slurping and utensil clanging, along with the occasional full-throated belch (true story!) and guess that there is eating going on inside. He might guess that eating probably involves a set of stages, primarily queuing in line to get served and sitting down to eat.

Major processes in the cafeteria

What might be a good model for serving? Maybe monks can get their dishes and utensils and work their way through the serving line at the rate of about 5 monks per minute. If 25 monks queued up at once, it would take 5 minutes before the line was empty again. The rate people are served does not really depend on how many people are in line.

Oh yes. I really did spreadsheet this up. Here is the chart of monks going in (orange) and out (blue) of the serving line versus time. Here the monks arrive in two bunches, one at the start of the hour, and one about 10 minutes later. The black line shows how many monks are waiting to be served. Monks are served at a rate of about 5 per minute. 25 minutes into the lunch service all the monks are now seated and eating. 

After each monk gets his meal, he takes a seat and starts eating. Personally I am a slow eater and was nearly always the last person to finish my meal (after about 25 minutes). If I had to guess, I would say the average time to eat was about 15 minutes, but I also saw some people literally throwing food into their mouth. There is probably a theoretical maximum speed that someone could inhale their food. I think I've witnessed close to it.

How long it takes monks to eat meals. Some are slower eaters (right side) some are faster (left side) but most people are somewhere in the middle. 

Putting it all together.  In this case, monks arrive at the cafeteria (brown) in two bunches. The first monks start finishing about 10-20 minutes later. The rate that monks leave the cafeteria is shown in green-blue. Substitute "monks arriving" with "precipitation falling" and "monks finishing" with "river flowing" and you're looking at the kind of charts that many hydrologists deal with all the time (called hyetographs and hydrographs). 

This fairly simple model probably captures the main things that influence how long people stay in the mess hall. Similarly, the core of nearly all hydrology models are the same or similar to eachother. Modelers call things like queuing and eating "processes", and hydrologists generally agree on what the major processes are (e.g. evaporation, infiltration, and so on).

So where does it all fall down? Why are there dozens upon dozens of different models out there? And why are they such a challenge to use for real-world forecasting?

[Tune in to part 2!]