part of EQUORA Institute
HUEN
EQUORA Institute · Technical working draft · Water

Scroll to the end and try every interaction → earn a Resonator Pass. 5 Passes = free attendance at an invitation-only Interference evening.

Mental Fast Food™ · Water

The Carpathian Basin
is drying

The basin is water-rich, and every year it is drier. Both statements are true, and the instrument we measure with cannot express the difference. What follows examines how the water balance concept should be developed toward an actual solution.

Source
This is the technical working paper — derivations, error propagation, institutional and decision-theoretic model. If the topic is new to you, start with the reader version: What the traditional water balance cannot see →
Starting material: Litkai Gergő: A hazai vízkassza Balatonokban · Data: OVF (National Water Directorate) · NASA GRACE-FO · OECD · State Audit Office · Hidrológiai Közlöny · KSH
Collaboration
EQUORA Institute × GoHalve
Updated
July 2026

Interference topic · Water-rich and drying — the same instrument

What if the instrument we measure with is itself what decides what we fail to see?

Development

How should the water balance concept become a practical decision tool?

Three steps from the flux balance to a decision framework

The Hungarian water balance is a good instrument. Consistent, sourced, with a decades-long time series — one of the best documented systems in the Carpathian Basin. However, this approach examines water scarcity from the same viewpoint as the approaches in use for decades: how much water passes through the country. In fact, a far more important question is how much water stays, for how long, and who decides about it. This material examines that in detail — in three steps, each of which uses the existing balance as its input.

Step 1

From the flux balance to the state balance

The water budget equation closes the system and provides decades of consistency. This is the starting point.

P + Q_be = E + Q_ki 58 + 114 = 52 + 120 km³/év
P = precipitation · Q_be = river inflow · E = evapotranspiration · Q_ki = river outflow. These four terms are the balance. Sources: OVF · MeRSZ · Hidrológiai Közlöny.

Where do these four numbers come from? All four items come from the water resource management publication of the Hungarian General Directorate of Water Management (OVF), as annual averages in cubic kilometres. The 114 and 120 are the sums of river discharge entering and leaving at the border sections; the 58 is precipitation falling on the country; the 52 is evaporation. The publication states neither the years it refers to nor which of the four are measured and which are computed — the exact closure of the balance (58 + 114 = 52 + 120 = 172) suggests that at least one item is derived from the others. That gap is precisely the subject of the next section.

All four terms are fluxes: quantities passing through per unit time. The state variable — S, the water actually stored — stays outside the balance:

dS/dt = P + Q_be − E − Q_ki

The balance measures the right-hand side of dS/dt, and from it infers the rate of change of S. This was a well-founded design decision at the time: in that era the relevant question was whether the water fits in the channel, and for that the flux is the correct quantity. Today's question concerns stored water, so S is needed as a quantity in its own right.

This matters because the “water-rich basin” claim rests on the 11,000 m³/capita/year figure, which is likewise a flux. Throughflow and stored water are two different things: two basins with identical throughflow but different residence times are in entirely different situations. Hence the need for the second quantity:

τ = S / Q

Its practical significance is the following. Retention policy — reservoirs, wetlands, a recharged soil profile — increases the residence time while the throughflow stays unchanged. The direction itself is not new: according to Válasz Online's reconstruction, plans for recharging the Homokhátság go back to a 1992 article in Petőfi Népe; WWF Hungary and Dalma Dedák have for years described the spiral of falling groundwater → illegal wells → further decline; István Láng, director-general of the OVF, spoke in autumn 2025 about the need for a paradigm shift toward retention in the hill regions; and Litkai Gergő's analysis closes on the same point: when do we finally stop draining and start retaining. It follows that introducing τ is what makes measurable the effect of precisely the intervention type these proposals share. Today's balance is sensitive to flux, while retention leaves its mark on the state — τ is the quantity that connects the two.

The question of uncertainty

The »domestically generated reserve« arises as the difference of two large numbers: 120 − 114 = 6 km³. So the question is what interval belongs to that 6. The answer is instructive, because the same institution publishes two different sets of figures.

OVF website · water resource management
no reference period stated
Q_be  114 km³/év
Q_ki  120 km³/év
P     58   E  52
6,0 km³/év · 600 m³/fő
Láng István, director-general of the OVF
autumn 2025 · via NAK / Qubit
Q_be   98 km³/év
Q_ki  105 km³/év
P     59   E  51
7,1 km³/év
The difference between the two inflow figures is 16 km³ — 2.7 times the derived quantity itself. Neither publication states a reference period or an interval, so the reader cannot tell whether this is a decline (consistent with the Danube's 10% and the Tisza's 30% discharge loss over ten years) or a methodological revision. The first set closes exactly (58 + 114 = 52 + 120 = 172); the second is off by 1 km³ (59 + 98 = 157 against 51 + 105 = 156).

The behaviour of the residual is worth attention. The flows moved by 15–16 km³ between the two publications, while the derived quantity moved by 1.1 (from 6 to 7.1). At this precision, the residual cannot resolve whether domestic generation rose, fell, or stayed put. The slider below shows the interval implied by a given gauge error, with both official values marked on the same axis.

Interactive · error propagation
Produce the interval yourself
Assume each gauge carries an independent relative error p. Then for the OVF website's figures σ = √((114p)² + (120p)²).
Gauge error p
5,0%
0 6,0 · ovf.hu 7,1 · főig. −40 +40 km³
Std. dev. σ
8,3 km³
Signal / noise 6÷σ
0,72
P(reserve ≤ 0)
23,4%

The 6 km³ is a good quantity — not merely a number — however, to judge how reliable it is and to make decisions with it, the error bound needs to be known as well. The interval tells us how large an intervention has to be for its effect to show up in the balance. The 0.6 km³/yr groundwater deficit quoted by the director-general is a case in point: it is a tenth of the reserve it is measured against.

Caveat. The 16 km³ gap is an observation, not an error estimate: it may well come from different reference periods, in which case it measures decline rather than uncertainty. The slider's own figure rests on our 5% and independence assumptions; correlated gauge errors partly cancel, so the true standard deviation is smaller. Precisely this is why the interval and the reference period would be worth publishing alongside the official value — with them, the two figure sets would become comparable.
The extension
  1. 1Bring the direct measurement of S into the national balance. The GRACE-FO satellite pair measures the mass anomaly — that is, the state itself — and the OVF's Nyírség model already computes in this framework (2010–2022: −5.21 km³ saturated volume, −102 cm average groundwater level). The data and the method are both available; what is needed is calibration against the groundwater monitoring network and inclusion in the balance.
  2. 2Compute and publish τ = S / Q per water body, as a time series. The denominator is available: the discharge series of the vizugy.hu gauging network. The water-body breakdown is available too: the delineation of the 3rd River Basin Management Plan (VGT3).
  3. 3State the reference period and the confidence interval for each of the four balance terms — precipitation (58), river inflow (114), evapotranspiration (52), river outflow (120) — and for the 6 km³ derived from them.
Step 2

From the national balance to a basin-scale decision framework

The closing point of Litkai Gergő's analysis of the five working examples is that everywhere the water bookkeeping was put in order first — measurement, price, entitlements, responsible institution — and the megaprojects cast in concrete only came afterwards. This ordering is correct, and the passage on the Murray–Darling identifies the role of the cap precisely as well: on paper, no more water can be allocated than is in the river, and here that account is unsettled with the hundred thousand illegal wells.

That statement holds within a national frame. The basin scale, however, adds an element the frame does not contain: the question of the responsible institution where the water arrives across a border.

When a policy conclusion is drawn from the balance, an optimisation problem is implicitly assumed which sits outside the balance:

max U(x) feltéve / s.t. x ∈ F

Three things are needed for this: a decision-maker, an objective function U, and a non-empty feasible set F. The balance's job is description, so these have to be placed alongside it.

The decision-maker at basin scale

If N actors share a resource without an enforcer, the non-cooperative equilibrium is over-abstraction, because the downstream externality is borne by actors other than the one abstracting. This equilibrium arises independently of the participants' intentions, so changing the attitude leaves the same equilibrium in place. This mechanism also explains the process reported by the OVF's deputy director-general: the Danube lost 10% and the Tisza 30% of its discharge in ten years. Those figures are produced at Hungarian gauging stations, while the underlying decisions are made in the upstream part of the catchment — and as a study in Hidrológiai Közlöny notes, the water resources generated beyond our borders, vital to us, are also used by the neighbouring countries, and this will only intensify.

The Australian reform worked because the Murray–Darling fell under a single legislature: one cap, one court, one enforcer. For the Carpathian Basin, this structural condition is what has to be created first — at present there are bilateral agreements, one per border section, without a basin-level authority or a Basin Plan.

From which a fixed ordering follows:

feasibility → optimality

On some water bodies along the Tisza, utilisation is above 100% according to the KvVM data, and the State Audit Office's report 25024 puts the number of unlicensed wells at up to a hundred thousand. The current state therefore lies outside the permitted set. In such a situation a market instrument prices uncovered claims. The water market is a good instrument — demonstrably so in Australia — but the order of its introduction is fixed: measurement and cap first, then trading.

The extension
  1. 1An abstraction cap per water body, with its error bound, placed alongside the balance. Both inputs exist: the VGT3 delineation supplies the unit, and the utilisation figures (46% nationally, above 100% on the Tisza water bodies) supply the baseline. What is missing is the cap itself, and the interval from step 1.
  2. 2Naming the smallest institutional unit able to set and enforce the cap — potentially with the jurisdiction of a single catchment, ahead of covering the whole basin.
  3. 3Allocation instruments, once the first two are in place.
Step 3

From estimates to the loss function

To the question of whether the basin is drying, the answer exists and is of good quality. GRACE-FO has measured continuously since 2002, and NASA warned in March 2026 on this basis about Hungary, Slovakia and the surrounding region; the OECD's 2026 report shows a −3%/yr trend in renewable freshwater between 2000 and 2023; the OVF's model computes −5.21 km³ of saturated volume and −102 cm of average groundwater level in the Nyírség between 2010 and 2022; the director-general of the OVF put the annual groundwater deficit at 0.6 km³, meaning 3–5 cm of decline; and the State Audit Office established 133.6 million m³/yr of unlicensed abstraction. This question can be regarded as settled.

Litkai Gergő's analysis records this itself when it observes that our strategic question has been the same for decades as it was in 1992. A decision-theoretic conclusion follows from that observation. The value of information is defined as:

VOI = E[U | döntés az új adat után] − E[U | döntés most]

If the posterior probability on a question is already effectively 1, then the information value of a further measurement on that question is close to zero. Since the answer exists, the information value has moved to another question, and the bottleneck has moved with it.

It moved to where the objective function stands. What awaits writing down is exactly what we lose, when, and what it is worth. Three concrete items where this is missing today: what the 3–5 metre groundwater decline on the Homokhátság costs, to whom, and over what horizon; what evapotranspiration is worth as a landscape service — the analyses in Hidrológiai Közlöny identify it as temperature regulation, and László Báder writes that sustaining the cooling of the landscape would require more additional water than the entire residential, industrial and agricultural demand combined; and the actual shadow cost of the 24.5% network loss measured by MaVíz. This U is what turns a measurement result into a decision. It is a normative question, so it comes about by being written — with value choices that have to be stated.

The limit of the past-based approach

The decomposition of the estimation error:

MSE = torzítás² + variancia

Over recent decades we have been reducing the variance: more gauging stations, better models, satellite series. That was the right direction. However, since the process is not stationary — according to the data in Hidrológiai Közlöny, evapotranspiration is rising by 0.42 mm per year, and in the 2022 drought year record low water levels fell one after another on the Danube at Dunaújváros, Dunaföldvár, Paks, Dombori and Baja — the bias grows meanwhile: the historical distribution we sample from differs from the one generating the future. The historical estimator thus remains consistent, but for a different quantity. Past data is precise, and it pertains to the system that existed at the time of measurement. The 114 versus 98 discrepancy in step 1 is the same phenomenon from the reader's side: a figure without a reference period cannot say which system it describes.

The extension
  1. 1Writing down an explicit loss function: stipulations, horizon, discount rate, and naming whose loss it is. The three items above are the starting set.
  2. 2Fixing the decision criterion in advance: stating which measurement result triggers which intervention.
  3. 3Scenario-based projection alongside historical extrapolation, in which the historical series serves as an input. The VGT3's climatic water deficit figures (up to 350 mm/yr in the middle of the Great Plain, 28 drought years out of 100) provide the baseline for this.

Summary — what the next version of the water balance would contain

The current balance states how much water passes through the country, and that answer remains an input to the next version as well. Three elements have to be added:

  1. 1S and τ alongside the fluxes, because retention shows up in these quantities, plus the reference period and error bound on the four balance terms — precipitation, river inflow, evapotranspiration, river outflow.
  2. 2An abstraction cap and the institution enforcing it, because feasibility precedes optimisation, and this is where the basin scale adds to the national frame.
  3. 3A loss function and a decision criterion fixed in advance, because the bottleneck has moved from measurement to the objective function.

All three are conceptual and institutional tasks. The data underlying them is already collected: the GRACE-FO series since 2002 gives the state; the OVF's Nyírség model supplies the method for deriving it; the vizugy.hu gauging network supplies the discharge series; the VGT3 supplies the water-body delineation and the climatic water deficit; the KvVM data supply utilisation per water body; the State Audit Office's report 25024 supplies the estimate of unlicensed abstraction; the KSH STADAT series supplies network loss; and Hidrológiai Közlöny supplies the methodology for evapotranspiration and for low-flow resource estimation. What is left to produce is the residence time, the interval, the cap, the institution, and the loss function.

Same research thread Global forecast to 2030 → Which water-saving move matters → Track your own footprint — GoHalve →

TakeawayA balance becomes a balance by measuring the stock as well as the flow. When you see a set of figures about a system, it is worth checking whether stock data sits beside throughput: with water this difference decides whether we know how much we have, or only how much passed through us.

Research provenance
This page comes out of research at the EQUORA Institute and captures one state of that work rather than a settled institutional position. That state rests on the findings available at the time of publication; later findings appear here only where the page has been updated, which the date shows. AI takes part throughout the research process as a thinking partner; responsibility for interpretation and publication remains human.
Published: 10 July 2026
Papp László · EQUORA InstituteHow We Research →
Scientific background
The Hungarian water balance, its sources, and the figures used on this page

The research is free — and will stay free. If it matters to you, there's a way to say so.

Support the work →