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SCIENCE · INVESTIGATE AND EXPLAIN

Stress-test water supply and timing

Inspect shortages, spill and storage across supplied dry, pulse and demand scenarios.

Learning outcome: Explain why finite storage and event order can prevent targets being fulfilled.

Starting recap

The dry and pulse schedules are original teaching stresses, not forecasts or drought classifications.

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Try

Dry release 5 gives 40 + 35 = 35 release + 40 service, with unmet service 100 m3.

Open the experiment

Predict

Which requests remain fulfilled as initial storage is depleted?

Experiment

Capture regular and dry cases, then inspect the first pulse bin and trace spill separately.

Allocate a bounded reservoir under stress

Fictional water-allocation policy · separate observed river record · Original fictional reservoir, capacity 100 m³ and initial storage 40 m³. Each daily bin receives all its supplied inflow, spills above capacity, prioritizes the requested downstream release, then supplies service demand from remaining water. No evaporation, groundwater, within-day hydraulics or forecast. Release targets are policy assumptions, not ecological adequacy thresholds. Unmet requests are not water fluxes. This model is not calibrated to the separate USGS river record.

Reset keeps your prediction, captures and practice history.

One reservoir, two requests and a fixed order

Regular inflow; service request 20 m³/day. This fictional store starts with 40 m³ and holds at most 100 m³. The requested controlled downstream release is 5 m³/day. The service request is 20 m³/day. These are supplied teaching conditions, not a real reservoir forecast or recommended ecological flow.

Predict before comparing: if you increase the release request under the same inflow scenario, what happens to service and storage? Treat your preferred allocation as a stated choice; the arithmetic does not decide whose needs should take priority.

  1. Receive the whole day's supplied inflow into the starting store.
  2. Spill any volume above 100 m³ before either requested allocation.
  3. Prioritize controlled downstream release, capped by the water available.
  4. Supply school/community service from the remaining water; retain the remainder for the next day.

This daily event order is a policy and timing assumption. It does not resolve within-day hydraulics. Changing the order could change spill or service. Evaporation, groundwater exchange and other losses are omitted.

Stored volume (m³): initial state and end-of-day snapshots020406080100Capacity 100 m³01234567Day 0 is initial storage; days 1–7 are after allocationLines guide the eye between snapshots; they are not within-day flow predictions.

Close the water ledger

Across seven days: 40 initial + 140 inflow = 0 spill + 35 controlled release + 140 service supplied + 5 final storage, all in m³. Balance residual: 0 m³.

Spill and controlled release both leave the store, but their timing and consequences need not be equivalent. More released water is not, by itself, evidence that ecological needs are met. Unmet requests are comparisons against a target, not additional water leaving the store.

Event order left to right; every quantity is m³ within the stated daily bin
DayStartInflowBefore spillSpillAfter spillControlled releaseAfter releaseService suppliedEndBalance residual
140206006055520350
235205505555020300
330205005054520250
425204504554020200
520204004053520150
615203503553020100
71020300305252050

Keep requests visible when water runs short

All volumes in m³; actual fulfillment plus shortfall equals the request
DayRelease requestedRelease actualRelease shortfallService requestedService suppliedUnmet service
155020200
255020200
355020200
455020200
555020200
655020200
755020200
Seven-day totals353501401400
Check a matched comparison and a timing counterexample

Worked comparison, separate from the current selection: under regular inflow, requesting 5 m³/day releases 35 m³, supplies all 140 m³ of service and leaves 5 m³. Requesting 10 m³/day releases 70 m³, supplies 110 m³ of service and leaves zero; unmet service rises to 30 m³. One reported indicator improves while another worsens. Choosing between these cases needs objectives and evidence beyond this ledger.

For the pulse case, day one begins with 40 m³ and receives 80 m³. The resulting 120 m³ exceeds capacity, so 20 m³ spills before allocations. Supplying service first would be a different timing model. Do not interpret the daily snapshot line as evidence that this pulse arrives gradually.

Transfer: keep the requested release at 5 m³/day and compare regular inflow with dry stress, then with higher service demand. Identify which input changed, show the complete water balance, and state one additional observation needed before proposing a real intervention. The separate USGS streamflow record is an observation audit; it does not calibrate these inputs or establish permitted withdrawals.

Final storage 5 m³; service supplied 140 of 140 m³ requested; unmet service 0 m³.

40 + 140 inflow = 0 spill + 35 controlled release + 140 service + 5 storage (m³). Requested controlled release 35 m³; release shortfall 0 m³. Priority and daily event order are assumptions, not a claim about the best policy.

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Ask how a plan fails under a stated stress

A policy that meets requests during one schedule may fail when inflow or demand changes. Keep the requested release at 5 m³/day and predict which output changes first when you switch from regular to dry inflow. Write a mechanism, such as storage supplying the initial difference between inflow and outflow, rather than simply predicting that the situation becomes worse.

Each scenario spans seven days with initial storage 40 m³ and capacity 100 m³. The dry schedule supplies 5 m³/day rather than the regular 20. It is a constructed stress test, not a statistical declaration of drought at a real location. No probability or recurrence interval is attached to it.

Follow the dry-case depletion

During the first dry day, 40 + 5 = 45 m³ is available. Release takes 5 and service takes 20, leaving 20. Day two starts with 20, receives 5, releases 5 and supplies 20, ending at zero. On each remaining day, the 5 m³ inflow fulfills the prioritized release, leaving no water for service.

Predict the seven-day totals before checking the visual: inflow 35, release 35, supplied service 40 and final storage zero. Requested service totals 140, so unmet service is 100. Conservation gives 40 + 35 = 35 + 40. The unmet 100 is a demand comparison, not missing physical water in the ledger.

Capture regular and dry settings separately. Explain why equal weekly release can coexist with very different service. The priority rule protects the smaller release request in this particular pair; it does not guarantee that every target can be met under every stress.

A larger request can also be unmet

Switch to dry inflow and release 10. Actual controlled release totals 45 m³, not the requested 70. Release shortfall is 25, service supplied is 30, unmet service is 110, and ending storage is zero. Check total actual outflows: 45 + 30 = 75, matching initial 40 plus inflow 35.

This comparison exposes two distinct targets and their shortfalls. A bar labeled requested release would mislead if it were presented as delivered release. Read the daily table to locate the transition from fulfilled targets to restricted delivery; do not infer an ecological outcome from the size of a target alone.

Compare timing and capacity constraints

Now select the pulse schedule with release 5. The first day receives 80 m³, so 40 + 80 exceeds capacity by 20. That 20 spills before either allocation. Afterward the reservoir releases 5 and supplies 20, ending the first day at 75. The remaining six days have zero inflow.

Over the week, spill is 20, controlled release 20 and supplied service 80, with zero ending storage. The balance is 40 + 80 = 20 + 20 + 80. Release shortfall is 15 and unmet service is 60. A large early inflow does not guarantee later service because capacity and operation timing matter.

The pulse and regular scenarios have different inflow totals, so they do not isolate timing alone. State that confound before comparing them. Within-day storage and outlet operation are also unresolved by the assumed receive-then-spill sequence. USGS water-budget guidance motivates explicit boundaries and storage; the supplied scenarios remain original teaching constructions.

Transfer: test capacity on paper

For a separate two-day case, use initial storage zero, capacity 10 m³, no release, service demand 5 m³/day and the same receive-then-spill order. Compare inflows [10,0] and [20,0]. Calculate service and spill. Does doubling inflow double supplied service? This paper case deliberately changes model constants and is not a selectable lab recipe.

Check the water-stress transfer

With [10,0], service is 5 each day and spill is zero. With [20,0], 10 spills immediately, then service is again 5 each day. Both supply 10 m³; the larger input does not increase service under the capacity and ordering assumptions. This public worked case tests timing and boundary reasoning, not a real reservoir design.

Apply

Pulse inflow 80 m3 with initial storage 40 and capacity 100 first produces:

Public practice checks a specific claim. It does not establish independent mastery.

Identify changed totals as a confound and avoid inferring within-day operations from daily bins.

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Compare reservoir allocation policiesNext: Read actual daily streamflow evidence
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