Uncertainty done properly: what to vary, how, and how to say it

Sort the uncertainties behind one number, choose a treatment for each, widen it into a band, and say it three ways

Research studio R6 of Energy Systems, Step by Step: sort twelve uncertainties into parameter, structural, scenario and deep, set apart the study’s own choices, pick a treatment for each, turn a single forecast into bands in your browser, rewrite it for a paper, a board and the public, and plan the uncertainty of your own study against the course rubric.
  • Researcher · L4
  • Research studio
  • 30 min guided · about 60 min practice
  • After M7 and M8

The task

  1. Produce: an uncertainty plan for your own study (each uncertainty, its kind, its treatment and how you will report it), and one result written as a range for a paper, a decision-maker and the public.
  2. From: a fictional study's single number, the twelve uncertainties behind it, and bands your browser computes on 2025's real hourly demand.
  3. Done when: the rubric's bar for Uncertainty: uncertainties classified; scenario or global sensitivity analysis; results as ranges.

About 30 minutes guided here, then about an hour on your own: sort your study's uncertainties, run one scenario or global sensitivity analysis, and write the result as a range for three readers.

The hour assumes your model already runs with its inputs ready; budget extra time to build one. No study yet? Plan Prairie Town's, adding two uncertainties this page leaves out.

Four kinds, and one pile set apart

  • Parameter: a number in the model that data or judgement can bound. Sample it with the others if you can defend its odds; with bounds only, compare low and high cases.
  • Structural: how the model is built, and what it leaves out. Run another form.
  • Scenario: an outside future with a few coherent versions. Run each, with no invented odds.
  • Deep: no agreed outcomes, odds or model. Show a what-if, and plan to adapt.
  • A choice, not an uncertainty: a decision or value judgement the study informs. Compare the options; never sample them.

The claim

“Prairie Town's peak demand will reach 515 MW in 2035.”

In this exercise the town accepts three car-uptake storylines but no odds for them, and no one can agree on a new customer's size or arrival. With other facts, a card could move pile.

Twelve uncertainties behind it, sorted, with reasons
Uncertainty Pile Why
How fast demand grows each year, apart from cars (0.4 to 1.6%) Parameter A number inside the model. Its range here is illustrative; a real study would set it from meter records. Give it a range, and odds if you can defend them.
How much energy one electric car draws on an average day (7 to 13 kWh) Parameter Another number inside the model. The range here is illustrative; a real study would need driving surveys or charger meter data to set it.
How hot the hottest afternoon of 2035 turns out to be Parameter Year-to-year weather is variability no study can know in advance. A real study takes its range from past years; the ±4% here is illustrative.
Whether car charging adds to the town's peak hour, or mostly to later hours Structural The form of the model: adding peaks assumes they come in the same hour; adding hour by hour does not. Run both forms.
Using 2025's hourly pattern of demand for every year to 2035 Structural A choice of structure (one year's pattern stands for all). Test it with another year's pattern, or state it as a limit.
Counting only cars charged at home, none charged at work Structural What a model leaves out is part of its structure. State it, and test a version with workplace charging.
How many electric cars the town has in 2035: 6,000, 15,000 or 30,000 Scenario Here the town accepts three storylines (car prices, models, policy) but no odds for them. Run each one; with odds you could defend, you could sample them.
Whether the state requires all-electric new homes after 2028 Scenario An outside policy path with two or three clear versions: a scenario, run one by one.
Whether a large new customer, such as a factory, asks to connect, and when Deep Here no one can agree on its size, its arrival or any odds. Show it as a separate what-if, and plan to adapt.
How travel changes if shared self-driving fleets arrive Deep Experts disagree on whether, when and how it changes charging: the outcomes themselves are unknown.
Whether the utility funds a managed-charging programme A choice, not an uncertainty A decision the study should inform. Run the study with and without it and compare; sampling it would hide the comparison.
How large a safety margin the utility plans above its forecast A choice, not an uncertainty A value judgement about risk. Show the range, and say what each margin implies; never average over margins.
Five treatments, one for each pile

1 · Parameter · How fast demand grows each year, apart from cars (0.4 to 1.6%)

  • Use the midpoint, 1.0% a year, and report one peak. Hard to defend. One number hides the range, and the reader cannot see how sure you are: the rubric's Developing level, “single numbers”.
  • Swing it from 0.4 to 1.6% with everything else fixed, as one bar of a tornado chart. Partly. A fair first screen, but a tornado chart moves one input at a time: it leaves most combinations unexplored and shows sensitivity to your chosen range, not the spread of outcomes.
  • Give it odds you can defend, sample it with the other parameters (Monte Carlo), report P10 to P90 and rank the inputs. Defensible. With odds you can defend, Monte Carlo moves all parameters together: the band shows the spread they imply (P10 to P90), and the ranking names the input that matters most.

2 · Structural · Whether car charging adds to the town's peak hour, or mostly to later hours

  • Widen the growth range until the band covers both model forms. Hard to defend. It hides a question about the model inside a parameter, and the band then answers neither.
  • Run both model forms and report the gap between them. Defensible. Sampling cannot reveal a structural choice; comparing forms can, and the gap tells readers how much the choice matters.
  • Use whichever form gives the higher peak, to be safe. Partly. Sometimes wise for a planner, but say so: readers would take a cautious bound for your best estimate.

3 · Scenario · How many electric cars the town has in 2035: 6,000, 15,000 or 30,000

  • Average the three and report the mean. Hard to defend. The average of three stories is a future nobody described, and it hides the spread between them.
  • Call the central one the forecast, and the other two the extremes. Partly. Fine if you can say why the central one is more likely; otherwise readers take a storyline for a prediction.
  • Run each one and show them side by side, with no odds attached. Defensible. Each storyline keeps its own band, and readers can see which assumptions drive the difference.

4 · Deep · Whether a large new customer, such as a factory, asks to connect, and when

  • Give it a 50% chance and add it to the sampled runs. Hard to defend. An invented 50% turns “we don't know” into a number that looks like knowledge, and it blurs the band for everyone.
  • Leave it out of the numbers, and mention it in the limits. Partly. Better than silence, but a 60 MW what-if is wider than much of the band: show it beside the result.
  • Show it as a separate what-if, look for a plan that holds with and without it, and name the signal that would trigger a review. Defensible. The approach of decision making under deep uncertainty: test plans across futures, and adapt when a signpost moves.

5 · A choice, not an uncertainty · Whether the utility funds a managed-charging programme

  • Sample it: half the runs with the programme, half without. Hard to defend. Mixing the two options blurs the very comparison the utility needs to make.
  • Run the study with and without the programme, and compare the two bands. Defensible. A choice is compared, not sampled: each option gets its own result, and the difference is what the programme is worth to the peak.
  • Assume the programme happens, since the utility has planned it. Partly. A plan is not a fact. Report the other case too, so readers can see what the programme changes.
The 2035 peak as bands, in numbers
Case P10 Median P90
The study's single number (peaks added, central, middle inputs) 515 MW
Peaks added, slow uptake 475 500 530
Peaks added, central uptake 490 515 545
Peaks added, fast uptake 510 535 565
Hours added, slow uptake 470 500 525
Hours added, central uptake 480 505 535
Hours added, fast uptake 495 520 550
What-if: a customer drawing a constant 60 MW from 2030 (hours added, central) median 565 MW

MW, rounded to 5; 1,000 runs, seed 6, each input drawn independently with equal odds across its range; no odds across the three uptake scenarios.

The claim rewritten for three readers (examples)
For a paper's results section
  • What varied: We drew growth (0.4–1.6% a year), a car's daily energy (7–13 kWh) and the year's weather (±4%) independently, with equal odds across each range, in 1,000 runs.
  • The range: Under central car uptake the 2035 peak is 480–535 MW (P10–P90 of the runs); under fast uptake, 495–550 MW.
  • Model form: Demand is added hour by hour on 2025's pattern; adding the two peaks instead raises the central median by 10 MW.
For the utility's board, which decides what to plan for
  • The range: Under central car uptake, about 9 in 10 model runs put the 2035 peak below 535 MW; under fast uptake, below 550 MW.
  • Not decided here: How much to plan for needs a reliability target and the cost of falling short; this forecast does not set them.
  • Not in the range: A customer drawing a constant 60 MW would raise each figure by 60 MW.
  • The signal: A connection request, or car numbers on the fast path, should trigger a new forecast.
For the public, in the town's newsletter
  • The range: If electric cars spread at a middle pace, about 8 in 10 of our model runs put the town's busiest hour in 2035 at 480 to 535 megawatts, compared with 450 in 2025.
  • What moves it: Faster spread shifts that range up, and higher values are possible. How fast demand grows matters most.
  • What it leaves out: A large new factory would add more.

With JavaScript on, you sort the cards, choose treatments, draw the bands yourself and write your own plan; your drafts stay in this browser.

Study: fictional. Its ranges, car numbers, charging patterns and the 60 MW customer are illustrative.
Hourly pattern: real. SPP's 2025 demand (EIA-930), scaled so the town's highest hour of 2025 is 450 MW, as in lesson 0.
Sampling: each input drawn independently, with equal odds across its range (an assumption of this illustration); 1,000 runs, seed 6.
Bands: P10 and P90 by linear interpolation, as in K5; rounded to 5 MW.

Two answers to the same task

Weak answer · Developing

Our model shows that Prairie Town's peak demand will reach 515 MW in 2035 [1]. We tested the sensitivity of the results and found them robust [2]. Electric cars add 18 MW to the peak [3]. Uncertainties remain, such as future policy [4].

  1. Falls short: One number, to the megawatt, with “will”: no range and no conditions.
  2. Falls short: Which inputs, over what ranges? “Robust” is asserted, not shown.
  3. Falls short: Only if charging and the peak come in the same hour: a structural choice left unstated.
  4. Falls short: Not classified and not treated: which ones matter, and what was done about them?

Strong answer · Proficient

Varied: growth (0.4–1.6% a year), a car's daily energy (7–13 kWh) and the year's weather (±4%), drawn independently with equal odds across each range, in 1,000 runs (seed 6) [1]. Scenarios: slow, central and fast car uptake, with no odds attached [2]. Model form: demand added hour by hour on 2025's pattern; adding peaks instead raises the central median by 10 MW [3]. Result: 480–535 MW (P10–P90) under central uptake, 495–550 MW under fast uptake [4]. Drivers: growth matters most (rank correlation 0.83), then weather (0.49) [5]. Not in the band: a customer drawing a constant 60 MW from 2030, shown as a what-if [6].

  1. Works: Parameters named, with their ranges and the sampling assumption: independent draws, equal odds across each range.
  2. Works: Scenarios kept apart, with no invented probabilities.
  3. Works: The structural choice stated, with what the other form changes.
  4. Works: Results as ranges, labelled as the central 80% of the modelled runs.
  5. Works: A global sensitivity ranking: rank correlation says how closely an input's ranking and the result's move together.
  6. Works: The deep uncertainty named and shown, not hidden in the band.
Weak answer Strong answer
The number One, with “will” Ranges, with what they mean
Uncertainties “Remain” Classified, each with a treatment
Model form Unstated Stated, with its effect
New customer Missing A separate what-if

Two rows of an uncertainty plan

Uncertainty Pile Treatment, and how you will say it Why
Weak row Future demand Parameter Sensitivity analysis. Too broad to treat: no range, no source, no way to say the result.
Strong row A car's daily charging energy, 7–13 kWh Parameter Range to set from charger meter records, with equal odds across it; sampled with the other inputs; reported as P10–P90, with its rank. One quantity, its range and source, how it is drawn, and how the result will be said.

The kinds compared

Kind What it is In this study Treatment How to say it
Parameter A number in the model that data or judgement can bound. Growth, a car's daily energy, the year's weather. With odds you can defend, sample together and rank the inputs; with bounds only, compare low and high cases. P10–P90 of the runs, or the bounded cases, with the ranges, odds and their sources.
Structural How the model is built, and what it leaves out. Peaks added or hours added; one year's pattern; home charging only. Run an alternative form, or benchmark against another model. The choice made, and the gap to the alternative.
Scenario An outside future with a few coherent versions. Slow, central or fast car uptake; a building code. Run each storyline separately. Side by side, with no odds unless you can defend them.
Deep No agreed outcomes, odds or model. A large new customer; self-driving fleets. Test plans across many futures; set signposts and triggers. A what-if beside the result, and the signal that would change the advice.
A choice (not an uncertainty) A decision or value judgement the study informs. Managed charging; the planning margin. Compare the options. One result per option.

Which treatment? Four questions in order

Ask them of each uncertainty in your list. The first yes gives its treatment.

Ask If yes
Your own choice? (a decision or a value) Compare the options (one result each)
In the model's form? Run another form (report the gap)
Odds you can defend? (a range, and how likely its values are) Sample it with the rest (P10–P90; rank inputs)
Bounds, or a few futures? Run each case (side by side, no odds)
None of these Deep: a what-if (robust plan, signposts)
Go deeperOther ways to sort uncertainty
  • Variability or lack of knowledge. A future year's weather varies however much you learn: sample it. This model assumes one constant growth rate; more history sharpens its estimate, but a future change may need its own scenario.
  • Data and measurement. Missing meter readings and revised statistics are uncertainties too; the cleaning log of R4 is where they are treated.
  • Values. A discount rate or a fairness weight is a judgement: show results across the choices, as for the utility's safety margin here.
Go deeperWhat this studio leaves out
  • Variance shares (Sobol indices) and Latin hypercube sampling: M7 and its notebook build them. Here a rank correlation is enough to rank three inputs.
  • Asking experts for ranges in a structured way (elicitation): a topic for a statistics course.
  • Decisions that hedge across scenarios (stochastic and robust optimization): M8.

Check your own work against the rubric

Competence Developing Proficient (the bar) Strong
Uncertainty
Look for: Your plan names each uncertainty's kind and its treatment, keeps your own choices apart, and your result is a range with what it means.		 Single numbers. Uncertainties classified; scenario or global sensitivity analysis; results as ranges. Decision-relevant uncertainty identified and its value discussed.

An uncertainty check for your own study

  • Listed: The inputs and assumptions that could change your answer, one line each.
  • Classified: Each tagged parameter, structural, scenario or deep; your own choices set apart.
  • Ranges sourced: Every range, and any odds across it, says where it comes from.
  • Varied together, if sampled: Parameters drawn together, not only one at a time, with their odds stated; inputs ranked by influence.
  • Scenarios apart: Each storyline run on its own, with no odds unless you can defend them.
  • Model form tested: At least one alternative form run, or the choice stated as a limit.
  • Results as ranges: Each range says what it is: a percentile interval of the runs, a scenario envelope or a bounded case; never a guarantee.
  • Honest digits: Numbers rounded to what the inputs support.
  • Deep ones named: What has no odds is shown as a what-if, with the signal that would trigger a review.

Myth or fact? “A tornado chart shows how uncertain a result is.”

  • Myth
  • Fact
Answer

Myth. It shows how far each input moves the result one at a time, over the ranges you chose, not how likely each outcome is.

Evidence: in a review of highly cited papers, 42% did not explore the space of inputs properly (Saltelli et al., 2019, abstract).

Myth or fact? “A Monte Carlo band gives the real-world chance of each outcome.”

  • Myth
  • Fact
Answer

Myth. It is only as good as the input ranges, the odds given across them, how they move together and the model's form. Call P10 to P90 the central 80% of the modelled runs.

Myth or fact? “When nobody knows the odds, ‘about as likely as not’ is an honest phrase.”

  • Myth
  • Fact
Answer

Myth. IPCC guidance gives that phrase a probability of 33 to 66%, and warns against using it to mean “we don't know”. Say what is unknown, and show it as a what-if.

Myth or fact? “The options a study compares should not be sampled like uncertain inputs.”

  • Myth
  • Fact
Answer

Fact. Each option gets its own result; mixing them in one band hides the difference the decision-maker needs.

Go deeper · ResearcherFrom Proficient to Strong: what knowing would be worth

Strong asks which uncertainty would change the decision, and what resolving it would be worth: the value of information. A toy with two equally likely futures (illustrative payoffs):

  • Plan A pays 12 or 2: an expected 7. Plan B pays 6 either way: an expected 6. Without a forecast, choose A.
  • With a perfect forecast you pick the better plan in each future: 12 or 6, an expected 9.
  • So a perfect forecast is worth at most 9 − 7 = 2 payoff units to someone who maximizes the expected payoff.

In the capstone research project (CR), your uncertainty plan goes into the proposal. M8 builds decisions that hedge before the uncertainty resolves; M7 builds the sampling.

Sources and what’s next

Numbers and data named on this page

Number or data What it is Source
2025 hourly demand SPP's demand, every hour of 2025: the real pattern the model adds car charging to. Its highest hour began at 16:00 on 29 July 2025 (Central daylight time). EIA-930, six-month files, SWPP · accessed 2 November 2026
450 MW Prairie Town's highest hour of 2025: the course's scale for the fictional town (lesson 0). The course's own convention
33 to 66% The probability the IPCC's calibrated language gives “about as likely as not” (Table 1). Mastrandrea et al. (2010)
42% Highly cited papers in Saltelli et al.'s review that did not explore the space of inputs properly (abstract). Saltelli et al. (2019)

Next

R7 · Cost and carbon done properly: one boundary, a fair baseline, a stated counterfactual

Sources and further reading

Spotted an error, or stuck? Write to hlli@ksu.edu. Corrections are made in place and dated here.

Text licensed CC BY 4.0, code MIT: teachers and students may reuse and adapt it, with credit to Honglin Li.