Modelling with Parsimony and Living with Prudence

 

[A bit of a technical blog – but with messages for you to decifer]

I went to see my Professor Friend at IIT Bombay. I had not taken his appointment. He was in the class teaching Water Quality Modelling to the postgraduate students.

When Professor saw me waiting outside, he paused and asked me to join.” Come in Dr Modak” he said, “I have just begun the first class”.

I took a seat in the last row.

Professor was introducing the basics of Streeter-Phelps model for modelling Dissolved Oxygen (DO) and Biochemical Oxygen Demand (BOD) in rivers.


For those who don’t know about the Streeter and Phelps  DO-BOD Model. The Streeter and Phelps model describes how DO decreases in a river or stream along a certain distance by degradation due to presence of BOD. The equation was derived by H. W. Streeter, a sanitary engineer at Cincinnati in the US, and Earle B. Phelps, a consultant for the U.S. Public Health Service. The model was built in 1925 based on field data from the Ohio River. The model makes use of two parameters viz. reaeration rate that depends on the hydraulic variables like depth and velocity and the deoxygenation rate that depends on the level and type of the organic matter present in the river.


Professor used few slides to explain the Streeter-Phelps model and the governing equations that attempted to explain the oxygen deficit. The model looked simple and rather straightforward asking for minimalistic data to help predict the outcomes.

“You can use this model for deciding the concentration of BOD that you could allow to ensure that we do not run into situation of high DO deficit that could affect the aquatic life”.

Professor solved one example problem the showed how limits to BOD can be set on this basis. He then expanded the problem statement to the case of multiple discharges of wastewater over a long river stretch with water withdrawals and tributaries joining.

He explained how the model can be used to decide not just the level of treatment of BOD but also decide on the minimum flow needed in the river to ensure dilution and assimilation of the wastewater.

Students enjoyed the application potential of the Streeter-Phelps model. Models must be taught with application perspective I said to myself.

Professor then paused and asked the students to critique the model. “Are we missing anything?” He asked one of the brighter students.

“Sir, I think the model misses the fact that wastewater contains suspended solids. These solids when settle in the bottom, the particulate BOD will reduce. We must include a sedimentation rate in the model. This rate  will depend on the river velocity at the point of wastewater discharge”

I thought he was right.

Another student commented “Well, whatever settles will still remain part of the system – the sediments at the bottom will continue exert an oxygen demand, albeit at a different degradation rate perhaps because the organisms responsible could be different”

“You are right” Professor said – we will recognize this aspect as Sediment Oxygen Demand (SOD).

A girl with spectacles got up and said – “How about the process of nitrification Sir?”

Professor said “Dr Modak, can I ask you to elaborate on this very important point?”

I liked this idea of participatory teaching. So, I walked to the blackboard and wrote the following

Ammonium in the wastewater is oxidized to nitrate under aerobic conditions as

NH4+ + 2O2 → NO3− + H2O + 2H+

Ammonium oxidation can be treated as part of BOD, so that BOD = CBOD + NBOD, where CBOD is the carbonaceous biochemical oxygen demand and NBOD is nitrogenous BOD.

The change in oxygen deficit due to oxidation of ammonium can be described with help of the nitrification rate and ammonium-nitrogen concentration. The model must expand.

The original humble Streeter-Phelps model thus started to look more complicated. And as if this was not enough, Professor introduced the role of photosynthesis and respiration. Photosynthesis and respiration are performed by algae and by macrophytes. Respiration is performed by bacteria and aquatic animals. Inclusion of photosynthesis brought the role of sunlight.

After some more brainstorming, all of us developed a bit monstrous water quality model (QUAL II) as shown below

Architecture of QUAL II model

“You can if you wish even further complicate this model – Professor said. “Maybe you like to build a model for a lake that is tending to be eutrophic (i.e. overloaded with nutrients and algae) and partially stratified during winter. This can be challenging” Professor winked.

The class was now about to end.

While summing up, Professor said “And friends, we can continue building more and more complex  water quality models for the interest of completeness. But remember that there is an optimal model complexity that we must recognize. Simpler is the model, more is the model uncertainty in prediction due to its frugal structure. But more is the model complexity, more are the parameters that come into play and hence predictions can become uncertain due parameter uncertainty. Imagine the complex model like QUAL II that requires data on more than 20 parameters (rates). Our poor understanding on these parameters can  lead to a “chaos” or “noise”, leading to a performance close to the simple  Streeter Phelps model. You must realize that your degradation rate in the simple Streeter and Phelps model will now become a surrogate with sedimentation and the reaeration rate will factor contribution due to photosynthesis on a “lumped basis”

I did know how much of this philosophy of modelling was understood by the students, but I was sure at least few did as the Professor projected his last slide.

When we reached Professor’s office, I asked for a coffee. Professor lighted his cigar.

“The most important message is understanding the Parsimony. The parsimony principle is basic to all science and tells us to choose the simplest scientific explanation that fits the evidence i.e. involves fewest entities. When scholar William Ockham wrote “Pluralitas non est ponenda sine necessitate” which later became known as the Law of Parsimony, it wasn’t to describe tightfisted stinginess but to say that all things being equal, the simplest explanation may times tends to be the right one. This realization is most important for a happy, successful and sustainable life”

I realized the topic had transcended the subject of water quality modelling

Professor took a deep puff

“I’m not saying that we don’t try to push ourselves to do the difficult or complex things in life. What it means is that we should look for the simplest way to achieve our goals and focus on the minimum but relevant tasks … while still doing them well. Remember – sometimes Streeter Phelps model can lead to same management decisions as arrived by a complex QUAL-II model”

He continued

“Some say parsimony means being stingy. I disagree. By saying “No, I can’t do that” may allow us to do what we want – that is really must be done or we would rather do – with our available time and energy. It has taken me many years to get my head around to “listen to myself”, look at my health and priorities of life”

“So, Professor, are you now living life on the principles of parsimony – that is hovering between complexity (due to your inherent curiosity) and a modest completeness (just good enough for your inner satisfaction?”. Professor did not answer. He looked outside the window.

I could not hesitate but ask “And have you reached the optima?”

“Well, Dr Modak, we will talk on this some other time. Needs another round of coffee” Professor got up from the chair. “I have to leave now as I have reach the meeting point for carpooling. See, I haven’t given up the comfort of riding a car but I am taking a simple step of sharing resources to reduce travel costs, curtail emissions and converse with new friends on topics other than environment. Its parsimony with prudence that makes life worth living and interesting

I understood now the significance of Streeter-Phelps equation. “Professor, when is the next lecture on water quality modelling?” I asked.

Professor smiled


Cover image sourced from https://www.linkedin.com/pulse/partial-least-squares-structural-equation-modeling-ali-asgari


Lift Kara De (LKD) is a carpooling initiative taken up by the enthusiastic residents of Whispering Palms Society in Kandivali, Mumbai, India. The group consists of about 256 carpoolers so far with numbers increasing every few months. Santosh Shetty, one of the key members of the Lift Kara De group had approached Ekonnect (my section 8 company) for calculating their individual/group emission reductions, fuel and money savings achieved so far from their ongoing carpooling activity.

Ekonnect team members estimated these values based on the data received from the LKD group members which comprised of number of rides, distance traveled, number of individuals in a car, type of fuel and years of carpooling.

The results showcased that in a short duration of 5 years LKD members had achieved 1, 91,000 Kg of Carbon dioxide emission reductions.

If you want to read this fascinating story , then do download this presentation


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8 thoughts on “Modelling with Parsimony and Living with Prudence

  1. All models are wrong, some are useful-says of Professor George Box, a great environmental statistician [ Refer Box -Cox Power transformation- I teach in the class]. My fried Mac Berthouex ( student of Box at Wisconsin Madison has gone further to use LP in water quality modeling. I am in entire agreement with Prasad. This is possibly the reason why I left Classical relational calculus, complex Markov and HMM ( after my PhD} and got into mathematically simple Fuzzy set theory wherein not only the parametric data but also expert’s perception is respected. What we need is human centric modeling and not just numerical data centric, -especially in Decision Research. I had long discussion on this aspect with my Guru and the father of Fuzzy logic in UC Berkeley during my academic visits.
    Take care of health Prasad. You are a jewel. and the world needs you for many many years.
    Ashok Deshpande

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  2. I find the simple Phelps model very much useful even after neglecting the role played by the constant k3 for taking management decisions. I have used the same in D. O. modelling of Nag River in Nagpur during the study of its rejuvenation. Having said this, I recognise the importance of complex models in understanding a particular phenomenon.

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