The Shifted Hydrological Template Relative Atmospheric–Terrestrial Alignment, ENSO Route Transfer, and a Prospective Spherical Registration Protocol in TSTOEAO
The Shifted Hydrological Template
Relative Atmospheric–Terrestrial Alignment, ENSO Route Transfer, and a Prospective Spherical Registration Protocol in TSTOEAO
DOI: [To be assigned]
John Swygert
July 31, 2026
Abstract
Global water conditions are commonly described through regional totals: rainfall above or below normal, rivers at high or low flow, reservoirs gaining or losing storage, and drought or flooding occurring within individual basins. These measurements are necessary, but they may conceal a more fundamental spatial relationship. The dominant atmospheric moisture-delivery architecture may shift, stretch, contract, intensify, slow, accelerate, or deform relative to the comparatively fixed geography of Earth’s surface. A modest displacement of a rain belt, storm track, monsoon boundary, atmospheric river corridor, or tropical convection center may remove dependable precipitation from one watershed while concentrating rainfall over another. The total atmospheric water supply need not change proportionally for the terrestrial expression to change dramatically.
This paper introduces the Shifted Hydrological Template Hypothesis within The Theory of Spatial-Temporal Observational-Expressional Architectural Orientation, TSTOEAO. The atmosphere is represented conceptually as a circumscribing hydrological field registered over Earth’s surface. The field is not proposed as a rigid physical shell. It is a mathematical and observational layer containing precipitation, moisture transport, circulation, pressure, temperature, and persistence patterns. Its position and geometry can be compared with the underlying arrangement of continents, mountains, watersheds, coastlines, snow zones, soils, vegetation, reservoirs, and groundwater systems.
El Niño and La Niña provide the most accessible demonstration. During El Niño, the center of tropical Pacific convection and rainfall shifts eastward as the Walker circulation changes; during La Niña, the western Pacific-centered circulation is generally strengthened. These changes alter atmospheric teleconnections, jet streams, and precipitation probabilities far from the tropical Pacific. They therefore demonstrate, at a basic level, that changing the relative position of an ocean-atmosphere circulation pattern can redirect rainfall without physically moving the continents. As of July 2026, NOAA reports a strengthening El Niño accompanied by enhanced convection over the central and east-central equatorial Pacific and suppressed convection over Indonesia, making the current event a timely observational case rather than prospective proof of the proposed framework.
The paper formalizes the hypothesis using spherical field registration. A reference hydrological template is transformed over the globe through rotation, longitudinal displacement, latitudinal migration, width change, amplitude change, seasonal phase shift, persistence, waviness, and regional deformation. Competing models are then tested to determine whether precipitation and water-storage anomalies are better explained by a displaced or deformed delivery architecture than by local intensity changes alone. The protocol integrates precipitation, atmospheric moisture transport, wind, pressure, temperature, river discharge, lake and reservoir levels, terrestrial water storage, snow, soil moisture, groundwater, and human water management. It preserves dimensional discipline by separating atmospheric water, energy, surface storage, discharge, and social consequences rather than adding unlike measurements into one artificial scalar.
The primary prospective prediction is that a preregistered transformation model fitted to atmospheric fields will predict withheld terrestrial precipitation and storage anomalies better than climatology, amplitude-only models, and nominal climate-index correlations. The framework is weakened if fitted shifts are unstable across datasets, fail to predict withheld regions and periods, or explain no more variance than unconstrained local changes. It is strengthened if measurable displacement and deformation parameters consistently precede and predict the migration of wet and dry anomalies, particularly near sharp climatic and topographic boundaries. The deepest proposition is not that Earth’s weather rotates as one rigid stencil. It is that the realized hydrological condition of a place depends upon its changing alignment with a mobile, deformable planetary delivery architecture.
1. Introduction
The same watershed can experience drought and flood within a single season.
A region may receive record rainfall while its reservoirs, groundwater, or soil moisture remain below normal.
A river may reach an extreme crest without producing durable basin recovery.
Another region may receive no spectacular drought event yet undergo years of declining lake, reservoir, snow, and groundwater storage.
These observations are often treated as separate local problems. Some result from precipitation deficits, some from heat and evaporation, some from water withdrawals, some from dam operations, some from land-use change, and some from brief extreme storms. All of those explanations may be correct. Nevertheless, the global distribution of high-water and low-water conditions invites a prior observational question:
> Is the principal change occurring only in the quantity of water delivered, or is the delivery architecture itself changing position and shape relative to Earth’s surface?
The distinction matters.
A rainfall field contains spatial gradients. One side of a boundary may receive persistent convection while the adjacent region remains dry. A storm track may repeatedly intersect one watershed and miss another. A monsoon margin may move across agricultural and river systems. An atmospheric river may make landfall tens or hundreds of kilometres north or south of its more typical corridor. Tropical rainfall may migrate with the Intertropical Convergence Zone, ITCZ. The centers of tropical Pacific convection may move longitudinally during the El Niño–Southern Oscillation, ENSO.
A comparatively small spatial change can therefore produce a disproportionate local result:
\[
\Delta X_{\mathrm{atmosphere}}\ \text{small}
\quad\rightarrow\quad
\Delta V_{\mathrm{basin}}\ \text{large}.
\]
The effect becomes especially strong where the precipitation gradient is steep or where geography creates thresholds:
a mountain crest;
a rain-shadow boundary;
a watershed divide;
a monsoon margin;
a freezing elevation;
a coastal landfall corridor;
a soil-infiltration threshold;
a reservoir catchment boundary.
A moisture pathway need not vanish globally for a basin to lose it locally.
The central visual model is simple. Imagine a globe surrounded by a transparent layer showing rainfall and atmospheric flow. Hold the continents stationary while shifting or rotating the atmospheric pattern slightly. Some land areas move out from beneath reliable moisture corridors. Others move beneath stronger precipitation. A third group remains within the wet pathway but receives water at a different season, intensity, duration, or phase.
This paper converts that visualization into a testable field-registration hypothesis.
2. Epistemic Status
The Shifted Hydrological Template Hypothesis operates at four distinct levels.
2.1 Established atmospheric and hydrological observation
Atmospheric rainfall patterns migrate, oscillate, deform, and vary in strength. ENSO alters tropical Pacific convection and influences atmospheric circulation globally. The ITCZ migrates seasonally and can shift in response to hemispheric thermal and energy imbalances. Hadley-cell boundaries, storm tracks, monsoons, subtropical highs, atmospheric rivers, and jet streams also change position and structure. These are established subjects of atmospheric science.
2.2 Conventional physical interpretation
The established mechanisms include:
ocean-atmosphere coupling;
sea-surface-temperature gradients;
atmospheric pressure gradients;
convection and latent heating;
angular-momentum transport;
atmospheric and oceanic heat transport;
Rossby-wave propagation;
land-ocean thermal contrast;
topographic lifting;
atmospheric moisture convergence;
radiative forcing;
soil and vegetation feedback;
snow and ice feedback;
ocean-current changes.
This paper does not replace those mechanisms.
2.3 TSTOEAO interpretation
TSTOEAO classifies the atmosphere, ocean, land, topography, vegetation, and water-storage systems as a changing relational architecture through which available water and energy become geographically expressed.
The basic grammar is:
\[
V=E\times Y,
\]
where:
\(E\) is available capacity, including atmospheric moisture, thermal energy, pressure gradients, and ocean-atmosphere energetic opportunity;
\(Y\) is the routing architecture, including circulation, position, geometry, timing, topography, phase, land condition, and storage capacity;
\(V\) is realized expression, including rainfall, snow, runoff, river flow, recharge, lake storage, drought, or flooding.
This is a second organizational map, not an alternative to meteorology or hydrology.
2.4 Prospective hypothesis
The genuinely new claim is methodological:
> A meaningful portion of global wet and dry anomalies may be represented and predicted as changes in the relative registration of a deformable atmospheric-hydrological field over Earth’s surface.
That claim has not yet been demonstrated by this paper.
It must be tested against simpler and more conventional alternatives.
3. The Circumscribing Hydrological Layer
Earth is not a perfect sphere. It is an oblate, irregular body whose gravity field, topography, oceans, and atmosphere vary spatially. Nevertheless, a spherical or ellipsoidal coordinate system is an appropriate first approximation for registering global atmospheric fields.
Let the planetary surface be represented as:
\[
\mathbb S^2
=
\left\{
\mathbf x:
\|\mathbf x\|=1
\right\}.
\]
Each surface coordinate is:
\[
\mathbf x=(\phi,\lambda),
\]
where:
\(\phi\) is latitude;
\(\lambda\) is longitude.
The hydrological layer is not a separate material membrane. It is an indexed collection of fields above and upon the surface:
\[
\mathcal H(\mathbf x,z,t)
=
\left[
P,\,
q,\,
\mathbf u,\,
\omega,\,
p,\,
T,\,
\mathrm{SST},\,
\mathrm{IVT},\,
C,\,
R
\right],
\]
where:
\(P\) is precipitation;
\(q\) is water-vapor concentration or specific humidity;
\(\mathbf u\) is horizontal wind;
\(\omega\) is vertical motion;
\(p\) is pressure;
\(T\) is temperature;
\(\mathrm{SST}\) is sea-surface temperature;
\(\mathrm{IVT}\) is vertically integrated vapor transport;
\(C\) is cloud or convective structure;
\(R\) is radiative state.
The word circumscribing means that these fields extend around the globe and can be represented relative to its surface. It does not mean that all weather exists in one altitude, moves as one rigid object, or is independent of the land and ocean below.
The hydrological layer is coupled to the surface:
\[
\mathcal H
\rightleftharpoons
\mathcal G,
\]
where \(\mathcal G\) represents the terrestrial-oceanic architecture:
\[
\mathcal G(\mathbf x,t)
=
\left[
h,\,
B,\,
S,\,
L,\,
V_g,\,
I,\,
W_h
\right].
\]
Here:
\(h\) is elevation and topography;
\(B\) is watershed and basin structure;
\(S\) is soil and infiltration condition;
\(L\) is land cover;
\(V_g\) is vegetation;
\(I\) is ice and snow state;
\(W_h\) is human water infrastructure and management.
The atmospheric layer acts upon the surface, and the surface modifies the atmospheric layer.
The relationship is recursive:
\[
\mathcal H^{(n)}
\rightarrow
\mathcal G^{(n+1)}
\rightarrow
\mathcal H^{(n+2)}.
\]
4. ENSO as the Basic Demonstration
El Niño and La Niña provide the most accessible large-scale example of a hydrological template changing relative to the continents.
ENSO is a coupled fluctuation of tropical Pacific ocean and atmosphere conditions that changes global atmospheric circulation and affects precipitation far beyond the equatorial Pacific. NOAA describes ENSO as one of Earth’s most influential climate phenomena because its tropical changes propagate into broader circulation and precipitation patterns.
4.1 Neutral or background Pacific architecture
Under broadly neutral tropical Pacific conditions:
easterly trade winds help maintain warmer surface water in the western tropical Pacific;
cooler water and upwelling characterize more of the eastern equatorial Pacific;
deep convection and heavy rainfall are concentrated more strongly over the western Pacific and Maritime Continent;
the Walker circulation links rising motion in the west with descending motion farther east.
This is not a static condition, but it supplies a reference architecture.
4.2 El Niño
During El Niño:
tropical Pacific sea-surface-temperature anomalies become warmer across the central or eastern equatorial Pacific;
trade-wind and pressure structures change;
the center of tropical convection can move eastward;
rainfall is enhanced farther east than under the background state;
convection and rainfall may be suppressed over portions of Indonesia and the western Pacific;
the altered tropical heating changes atmospheric wave patterns and teleconnections.
NOAA’s July 9, 2026 diagnostic reported strengthening El Niño conditions, enhanced convection over the central and east-central equatorial Pacific, and suppressed convection over Indonesia. This is a direct contemporary example of tropical rainfall expression shifting longitudinally relative to land and ocean geography.
In the simplest spatial language:
\[
\lambda_{\mathrm{convection}}
\rightarrow
\lambda_{\mathrm{convection}}+\Delta\lambda_E.
\]
The movement is not uniform at every latitude and altitude. Nevertheless, an eastward displacement parameter captures a major component of the reorganization.
4.3 La Niña
During La Niña, the coupled tropical Pacific state generally shifts in the opposite direction:
cooler-than-normal central or eastern equatorial Pacific waters;
stronger easterly trade-wind influence;
a more strongly west-centered warm pool and convective region;
altered global teleconnections and precipitation probabilities.
La Niña should not be treated as a mathematically perfect inverse of El Niño. Event strength, location, ocean background state, season, and interactions with other climate modes affect each outcome. ENSO events display substantial diversity, and similar Niño indices do not guarantee identical global precipitation patterns.
4.4 ENSO as a knob
ENSO is therefore not one knob controlling all weather. It is one major control dimension.
At the simplest level:
\[
\Theta_{\mathrm{ENSO}}
=
\left[
\Delta\lambda_{\mathrm{convection}},
A_{\mathrm{Walker}},
A_{\mathrm{SST}},
A_{\mathrm{teleconnection}}
\right].
\]
Changing this vector alters the registration of tropical heating and rainfall relative to Earth’s land and ocean arrangement.
The resulting global expression can include:
\[
\Delta V
=
\left[
\Delta P,\,
\Delta T,\,
\Delta\mathrm{storm\ track},\,
\Delta\mathrm{snow},\,
\Delta Q_{\mathrm{river}},\,
\Delta S_{\mathrm{water}}
\right].
\]
ENSO is thus the clearest introductory case for the broader hypothesis:
> Keep the globe fixed, alter the atmospheric-oceanic relationship, and the terrestrial water expression changes.
5. From One Knob to a Bank of Knobs
The full hydrological template cannot be controlled by one left-right rotation.
A better model contains a bank of independently measurable transformations.
5.1 Longitudinal displacement
\[
\Delta\lambda
\]
represents east-west movement.
Applications include:
ENSO-related tropical convection;
Walker-circulation changes;
ocean-basin rainfall centers;
longitudinal movement of subtropical highs;
storm-track landfall corridors.
5.2 Latitudinal displacement
\[
\Delta\phi
\]
represents north-south migration.
Applications include:
ITCZ movement;
monsoon-margin movement;
subtropical dry-zone movement;
storm-track and atmospheric-river landfall changes;
seasonal rain-belt migration.
The ITCZ contains a large fraction of global precipitation within a narrow tropical band, so modest positional changes can produce strong local rainfall differences. Research has repeatedly emphasized that the sharp rainfall gradient at the ITCZ margins makes small shifts hydrologically consequential.
5.3 Width
\[
w
\]
represents expansion or contraction of a circulation or rainfall belt.
A rain belt may remain centered at nearly the same latitude while becoming wider or narrower. A subtropical dry zone may expand. A monsoon region may cover more or less area.
Center position and width must therefore remain separate.
5.4 Intensity
\[
a
\]
represents amplification or weakening.
The pattern may remain geographically similar but carry:
more water vapor;
greater precipitation intensity;
stronger winds;
stronger moisture convergence;
weaker or stronger subsidence.
A shift-only model cannot explain every anomaly.
5.5 Seasonal phase
\[
\delta s
\]
represents earlier or later seasonal arrival.
A monsoon could deliver a similar annual total while beginning later, ending earlier, or concentrating more strongly within fewer weeks.
The annual total would conceal the change.
5.6 Translation speed
\[
v_T
\]
represents how quickly the pattern moves.
A rapidly moving storm may provide moderate rainfall. A slow or stalled system may produce extreme accumulation over the same location.
5.7 Persistence
\[
\tau_P
\]
represents how long the pattern remains registered over a region.
Hydrological damage may arise not only from intensity but from duration:
\[
V_{\mathrm{flood}}
\sim
P\times\tau_P.
\]
Likewise, drought may arise from persistent exclusion from moisture pathways.
5.8 Waviness and deformation
\[
\mathcal W
\]
represents departures from a smooth belt or simple translation.
Jet streams, storm tracks, convergence zones, and pressure systems may:
become more sinuous;
split;
merge;
form regional lobes;
develop stationary waves;
create alternating wet and dry sectors.
5.9 Vertical structure
\[
Z_H
\]
represents the height and vertical depth of the moisture and circulation field.
Two conditions with similar surface precipitation may differ in:
moisture depth;
cloud-base height;
freezing level;
convective depth;
vertical shear;
upper-level divergence.
5.10 Hydrometeor phase
\[
\Pi
=
\left[
P_{\mathrm{rain}},
P_{\mathrm{snow}},
P_{\mathrm{ice}}
\right].
\]
A moisture pathway may remain spatially aligned with a mountain watershed while warmer temperatures change precipitation from snow to rain.
The location of delivery remains similar, but the storage architecture changes.
5.11 Moisture-source composition
\[
M_S
\]
represents the source regions contributing water vapor:
tropical ocean;
subtropical ocean;
continental evapotranspiration;
recycled basin moisture;
polar or midlatitude sources.
Atmospheric-river research increasingly distinguishes source regions and transport regimes rather than treating every corridor as one identical phenomenon.
5.12 Surface-response controls
The same rainfall template can produce different outcomes depending upon:
\[
\Theta_{\mathrm{surface}}
=
\left[
S_{\mathrm{soil}},
V_{\mathrm{vegetation}},
U_{\mathrm{urban}},
F_{\mathrm{fire}},
I_{\mathrm{ice}},
R_{\mathrm{reservoir}},
G_{\mathrm{groundwater}}
\right].
\]
Thus, the full metaphor is not one knob rotating one immutable shell.
It is a bank of relational controls adjusting a mobile and deformable field over an uneven and changing surface.
6. Mathematical Representation of the Template
Let:
\[
P_0(\mathbf x,s)
\]
represent a reference precipitation climatology at surface location \(\mathbf x\) and seasonal phase \(s\).
Let:
\[
P_{\mathrm{obs}}(\mathbf x,t)
\]
represent observed precipitation at time \(t\).
The simplest Shifted Hydrological Template model is:
\[
P_{\mathrm{obs}}(\mathbf x,t)
\approx
a(t)
P_0
\left(
\mathcal T_{\Theta(t)}^{-1}\mathbf x,
s(t)+\delta s(t)
\right)
+
\epsilon(\mathbf x,t),
\]
where:
\(a(t)\) is an intensity multiplier;
\(\mathcal T_{\Theta(t)}\) is the spatial transformation;
\(\delta s(t)\) is seasonal-phase displacement;
\(\epsilon\) is unresolved residual structure.
6.1 Rigid spherical rotation
The most literal version of the user’s visualization is:
\[
\mathcal T_{\Theta}
=
\mathbf R(\alpha,\beta,\gamma),
\]
where \(\mathbf R\) is a three-dimensional rotation matrix defined by Euler angles:
\(\alpha\);
\(\beta\);
\(\gamma\).
This asks:
> How well can the observed rainfall anomaly be reproduced by turning the reference field over the globe?
This is intentionally simple and probably incomplete.
Its value is that it supplies a strict baseline.
6.2 Axis-specific displacement
The next model separates longitudinal and latitudinal movement:
\[
\mathcal T_{\Theta}
:
(\phi,\lambda)
\mapsto
\left(
\phi+\Delta\phi,\,
\lambda+\Delta\lambda
\right).
\]
This is better suited to ENSO-like longitudinal shifts and ITCZ-like latitudinal shifts.
6.3 Deformable field
A more realistic transformation is:
\[
\mathcal T_{\Theta}
:
\mathbf x
\mapsto
\mathbf x+\mathbf u(\mathbf x,t),
\]
where:
\[
\mathbf u(\mathbf x,t)
=
\left[
u_\phi(\mathbf x,t),
u_\lambda(\mathbf x,t)
\right]
\]
is a spatial displacement field.
The field can represent:
regional north-south migration;
east-west movement;
stretching;
compression;
curvature;
splitting;
localized stagnation.
The transformed template becomes:
\[
P_{\mathrm{shift}}
(\mathbf x,t)
=
a(\mathbf x,t)
P_0
\left[
\mathbf x-\mathbf u(\mathbf x,t),
s+\delta s(\mathbf x,t)
\right].
\]
6.4 Residual field
The complete observation is:
\[
P_{\mathrm{obs}}
=
P_{\mathrm{shift}}
+
P_{\mathrm{local}}
+
R_P.
\]
Here:
\(P_{\mathrm{shift}}\) is the component explained by displacement or deformation;
\(P_{\mathrm{local}}\) is locally generated intensification or weakening not reducible to displacement;
\(R_P\) is unresolved residual.
This decomposition prevents the hypothesis from claiming that every rainfall anomaly is merely a translated older pattern.
7. A Hierarchy of Competing Models
The hypothesis must outperform simpler alternatives.
Model 0: seasonal climatology
\[
M_0:
P=P_0(\mathbf x,s).
\]
No anomaly or transformation is included.
Model 1: local amplitude
\[
M_1:
P=a(\mathbf x,t)P_0.
\]
Rainfall increases or decreases locally without positional movement.
Model 2: global rigid rotation
\[
M_2:
P=a(t)P_0(\mathbf R^{-1}\mathbf x).
\]
The whole reference pattern rotates over the globe.
Model 3: zonal and meridional displacement
\[
M_3:
P=a(t)
P_0
\left(
\phi-\Delta\phi,
\lambda-\Delta\lambda
\right).
\]
Model 4: belt-specific transformation
\[
M_4:
P=
\sum_k
a_k
P_{0,k}
\left[
\mathcal T_k^{-1}\mathbf x
\right].
\]
Separate transformations are fitted for:
tropical convection;
subtropical dry zones;
midlatitude storm tracks;
monsoon regions;
polar precipitation.
Model 5: deformable field
\[
M_5:
P=
a(\mathbf x,t)
P_0
\left[
\mathbf x-\mathbf u(\mathbf x,t)
\right].
\]
Model 6: coupled atmospheric model
\[
M_6:
P
=
\mathcal F
\left[
\mathrm{SST},
\mathrm{IVT},
\mathbf u,
p,
T,
\omega,
\mathcal G
\right].
\]
This model includes physical predictors directly rather than relying primarily upon pattern registration.
Model 7: unconstrained statistical or machine-learning model
\[
M_7:
P=
\mathcal M_{\mathrm{flexible}}(\mathbf X).
\]
This supplies a high-flexibility benchmark.
The Shifted Hydrological Template hypothesis gains value only if the transformation parameters improve prediction while remaining stable, interpretable, and substantially simpler than a fully unconstrained model.
8. Basin Capture
Rain falling over the ocean, over a closed desert basin, over a snow-producing mountain range, or over an urban surface does not produce the same hydrological expression.
For basin \(b\), define a spatial capture function:
\[
C_b(\mathbf x)
=
\begin{cases}
1,&\mathbf x\in b,\\
0,&\mathbf x\notin b.
\end{cases}
\]
The direct precipitation exposure of the basin is:
\[
I_b(t)
=
\int_{\mathbb S^2}
P(\mathbf x,t)
C_b(\mathbf x)\,dA.
\]
Under a shifted template:
\[
I_b(\Theta,t)
=
\int_{\mathbb S^2}
P_0
\left(
\mathcal T_\Theta^{-1}\mathbf x
\right)
C_b(\mathbf x)\,dA.
\]
The basin does not move.
The atmospheric field moves or deforms relative to it.
8.1 Boundary amplification
The sensitivity of the basin to a template displacement is:
\[
\frac{\partial I_b}
{\partial\Theta}.
\]
This sensitivity becomes large when:
the basin lies near a strong precipitation gradient;
a moisture corridor runs near the basin edge;
mountain orientation sharply separates wet and dry slopes;
the basin depends upon a narrow seasonal window;
snow accumulation occurs near the freezing threshold.
A small atmospheric displacement may therefore have little effect on one basin and a major effect on another.
8.2 Topographic capture
A mountain range converts horizontal moisture transport into precipitation through uplift.
A simplified response is:
\[
P_{\mathrm{oro}}
=
f
\left[
\mathrm{IVT},
\mathbf u\cdot\nabla h,
T,
q
\right].
\]
A small change in wind or moisture-corridor direction can shift precipitation:
from one slope to another;
from one watershed to another;
from snow to rain;
from stored mountain water to immediate runoff.
Research on ENSO teleconnections in western North America shows that topography can amplify and spatially reorganize broad circulation-driven precipitation effects.
9. From Rainfall to Durable Water
Rainfall is an input, not the final water condition.
For a basin:
\[
\frac{dS_b}{dt}
=
P_b
+
Q_{\mathrm{in}}
-
ET_b
-
Q_{\mathrm{out}}
-
W_b
+
H_b,
\]
where:
\(S_b\) is stored water;
\(P_b\) is precipitation;
\(Q_{\mathrm{in}}\) is incoming surface or subsurface flow;
\(ET_b\) is evapotranspiration;
\(Q_{\mathrm{out}}\) is outgoing discharge;
\(W_b\) is human withdrawal;
\(H_b\) includes human transfers, releases, or impoundment.
Storage includes multiple reservoirs:
\[
S_b
=
S_{\mathrm{snow}}
+
S_{\mathrm{soil}}
+
S_{\mathrm{surface}}
+
S_{\mathrm{groundwater}}
+
S_{\mathrm{biological}}.
\]
A flood can occur while:
\[
\frac{dS_{\mathrm{groundwater}}}{dt}
\leq0.
\]
A reservoir may rise while regional soil moisture remains low.
Heavy rainfall may run quickly into the ocean rather than recharge an aquifer.
The relevant retention efficiency is:
\[
\eta_{\mathrm{retention}}
=
\frac{\Delta S_{\mathrm{durable}}}
{P_{\mathrm{positive\ anomaly}}}.
\]
This value depends upon:
rainfall rate;
storm duration;
soil saturation;
soil compaction;
vegetation;
fire history;
snow conditions;
basin geometry;
reservoir capacity;
groundwater permeability;
withdrawal;
operating rules.
The Shifted Hydrological Template therefore has two stages:
\[
\text{atmospheric delivery}
\rightarrow
\text{terrestrial conversion}.
\]
10. TSTOEAO Translation
The planetary hydrological expression can be written conceptually as:
\[
V_H
=
E_H\times Y_H.
\]
Here:
\[
E_H
=
\left[
\text{available atmospheric moisture},
\text{thermal energy},
\text{pressure-gradient capacity}
\right].
\]
The relational architecture is:
\[
Y_H
=
\left[
\text{circulation},
\text{position},
\text{orientation},
\text{timing},
\text{topography},
\text{temperature},
\text{soil},
\text{storage},
\text{human routing}
\right].
\]
The realized expression is:
\[
V_H
=
\left[
\text{rain},
\text{snow},
\text{runoff},
\text{recharge},
\text{flood},
\text{drought},
\text{storage}
\right].
\]
The expanded sequence is:
\[
\boxed{
\text{ocean-atmosphere state}
\rightarrow
\text{circulation route}
\rightarrow
\text{moisture transport}
\rightarrow
\text{geographic interception}
\rightarrow
\text{surface conversion}
\rightarrow
\text{water storage or loss}
}
\]
Each expression becomes architecture for the next stage:
\[
V^{(n)}
\rightarrow
Y^{(n+1)}.
\]
For example:
\[
V_{\mathrm{rain}}
\rightarrow
Y_{\mathrm{soil\ saturation}}
\rightarrow
V_{\mathrm{runoff}}.
\]
Then:
\[
V_{\mathrm{runoff}}
\rightarrow
Y_{\mathrm{river/reservoir}}
\rightarrow
V_{\mathrm{storage\ or\ flood}}.
\]
11. Route Transfer Rather Than Disappearance
The central TSTOEAO prediction is not that every lost millimetre of rainfall in one region must appear as exactly one additional millimetre in another.
That would ignore:
atmospheric storage;
ocean evaporation;
terrestrial evapotranspiration;
radiative and thermodynamic changes;
residence time;
precipitation efficiency;
phase changes;
transport between time windows;
changes in total atmospheric moisture.
The more defensible statement is:
> When a previously active delivery route weakens, the associated atmospheric water and energy budget should produce measurable changes in one or more alternative transport, storage, precipitation, evaporation, or residual channels.
A moisture-route accounting vector is:
\[
\mathbf R_H
=
\begin{bmatrix}
F_{\mathrm{vapor}}\\
P_{\mathrm{rain}}\\
P_{\mathrm{snow}}\\
ET\\
Q_{\mathrm{runoff}}\\
\Delta S_{\mathrm{atmosphere}}\\
\Delta S_{\mathrm{land}}\\
F_{\mathrm{ocean-land}}\\
R_{\mathrm{unresolved}}
\end{bmatrix}.
\]
These quantities must not be added casually unless they are expressed over compatible area, time, and mass units.
A legitimate water-mass budget can be expressed in units such as:
\[
\mathrm{kg\,s^{-1}}
\]
or:
\[
\mathrm{mm\,day^{-1}}
\]
over a defined region.
River stage, reservoir percentage, temperature, rainfall rate, and drought classification cannot be added directly.
12. Cost Location
In TSTOEAO, “cost” does not imply moral punishment or lost energy alone. It identifies where the consequences of a route appear.
12.1 Persistent exclusion
A basin repeatedly missed by moisture pathways may express cost through:
falling river baseflow;
reservoir decline;
groundwater extraction;
soil desiccation;
ecosystem stress;
agricultural loss.
12.2 Pulse delivery
A basin struck by concentrated rainfall may express cost through:
flash flooding;
erosion;
infrastructure damage;
sediment transport;
poor infiltration;
rapid ocean discharge.
12.3 Phase conversion
A mountain watershed receiving rain instead of snow may express cost through:
reduced seasonal snow storage;
earlier runoff;
lower warm-season water availability;
greater winter flood risk.
12.4 Mis-timed delivery
The annual total may appear normal while agricultural or ecological water arrives outside the required seasonal window.
12.5 Human amplification
Dams, diversions, groundwater pumping, drainage, urban surfaces, deforestation, irrigation, and land degradation may amplify or suppress the atmospheric signal.
The atmospheric template is therefore not solely responsible for the final cost.
13. Empirical Motivation
The World Meteorological Organization’s 2024 global water assessment found widespread departures from normal across rivers, lakes, reservoirs, groundwater, and glaciers, with flooding in some regions and severe drought in others. WMO reported that only about one-third of global river basins were near normal in 2024, continuing a multiyear pattern of hydrological imbalance. These observations motivate a global spatial analysis but do not by themselves establish that the anomalies arise from one shifted template.
A 2026 study of ITCZ migration reinforces the relevance of positional change. It reports that even modest ITCZ movement can strongly alter drought and flood distributions and examines how atmospheric and oceanic heat transport influence the location of the rain belt. The authors emphasize competing influences, including hemispheric temperature contrasts, Hadley-cell asymmetry, ocean heat transport, ENSO, and possible changes in Atlantic overturning.
Atmospheric rivers provide another example. They are concentrated corridors of water-vapor transport that can deliver major precipitation and flooding when they intersect coastlines and topography. Studies report changes in their frequency, intensity, source regions, and landfall patterns, including regionally opposing historical trends.
These findings support the plausibility of positional and geometric hydrological change.
They do not yet establish that one globally registered transformation explains the present pattern of high and low water.
14. Observational Architecture
A valid test requires multiple independent observation systems.
14.1 Precipitation
NASA’s IMERG product combines data from the Global Precipitation Measurement satellite constellation to estimate precipitation over most of Earth’s surface. Current products provide fine spatial and temporal coverage suitable for tracking moving rainfall structures.
Additional precipitation products should be included to test dataset dependence.
14.2 Atmospheric circulation and moisture
ERA5 provides reanalysis fields including:
atmospheric wind;
pressure;
temperature;
precipitation;
soil moisture;
sea-surface temperature;
vertical atmospheric structure.
ERA5 extends from 1940 to the present, permitting long historical comparisons, although reanalysis is model-assimilated rather than a pure observation.
14.3 Terrestrial water storage
GRACE and GRACE Follow-On estimate changes in terrestrial water storage from changes in Earth’s gravity field. Terrestrial water storage integrates groundwater, soil moisture, surface water, snow, and ice at broad spatial scales.
14.4 Rivers and lakes
SWOT products provide measurements and derived estimates for:
lake water-surface elevation;
lake area;
lake storage change;
river elevation;
river width;
river slope;
river discharge.
These measurements are particularly valuable for connecting atmospheric transformations to surface-water response.
14.5 Ground observations
Satellite and reanalysis data must be compared with:
rain gauges;
snow stations;
river gauges;
reservoir records;
groundwater wells;
local meteorological networks.
No single product is sufficient.
14.6 Dataset disagreement
A 2026 global assessment found that leading hydrological datasets can show low water-balance consistency when precipitation, evapotranspiration, runoff, and soil-moisture products are combined. Satellite precipitation products performed comparatively well across many tropical and subtropical regions, while gauge products performed better in some densely observed Northern Hemisphere regions. The result requires ensemble analysis rather than treating one dataset as unquestionable truth.
The observer architecture must therefore include uncertainty as part of the result:
\[
V_{\mathrm{measured}}
=
V_{\mathrm{hydrological}}
\times
Y_{\mathrm{observation}}.
\]
15. The Transformation Vector
The proposed planetary transformation state is:
\[
\Theta_H(t)
=
\begin{bmatrix}
\alpha\\
\beta\\
\gamma\\
\Delta\phi_k\\
\Delta\lambda_k\\
w_k\\
a_k\\
\delta s_k\\
v_k\\
\tau_k\\
\mathcal W_k\\
Z_k\\
\Pi_k
\end{bmatrix}.
\]
The index \(k\) identifies different circulation regimes:
tropical convection;
ITCZ;
regional monsoon;
subtropical dry belt;
midlatitude storm track;
atmospheric-river corridor;
polar or high-latitude precipitation field.
The global rotation angles \(\alpha,\beta,\gamma\) test the simplest shell-turning idea.
The regional terms test whether the apparent global shift is actually a combination of differently moving subsystems.
16. Prospective Experimental Protocol
16.1 Objective
Determine whether a preregistered spherical-registration model can predict withheld precipitation, river-flow, lake-storage, and terrestrial-water-storage anomalies better than non-positional alternatives.
16.2 Reference period
Two parallel reference climatologies should be constructed.
Short high-resolution baseline
Use the overlapping satellite era for high-resolution precipitation and surface-water analysis.
Long reanalysis baseline
Use a longer ERA5 and gauge-supported period for decadal and multidecadal comparison.
Results must be reported separately before any combined interpretation.
16.3 Spatial resolution
The analysis should be performed at multiple scales:
global;
circulation-belt;
continental;
major-river-basin;
sub-basin;
high-resolution topographic regions.
A transformation that appears strong globally may fail locally.
A local displacement may disappear when averaged globally.
16.4 Temporal resolution
The protocol should analyze:
daily;
weekly;
monthly;
seasonal;
annual;
multiyear windows.
Different hydrological components respond at different speeds.
16.5 Exploratory period
The exploratory dataset is used to:
establish transformation algorithms;
estimate parameter ranges;
determine spatial smoothing;
select regularization;
define uncertainty;
identify likely lags between atmosphere and storage.
16.6 Preregistration
Before confirmatory analysis, lock:
datasets;
preprocessing;
baseline periods;
transformation classes;
spatial regions;
withheld years;
withheld basins;
prediction metrics;
uncertainty thresholds;
failure conditions;
permitted model revisions.
16.7 Withheld temporal tests
Fit the transformation model on earlier years and predict later years not used in parameter estimation.
A rolling-origin test should repeatedly train on the past and predict the next season or year.
16.8 Withheld spatial tests
Fit atmospheric transformation parameters over oceanic and large-scale circulation fields.
Then predict rainfall and storage anomalies over withheld land regions or river basins.
This is critical because a model that sees the target basin during fitting may simply reproduce its anomaly.
16.9 Cross-dataset replication
Repeat the analysis using multiple precipitation, circulation, storage, and runoff products.
A valid pattern should not depend entirely upon one measurement system.
16.10 Current ENSO test
Because El Niño was already present by July 2026, the event cannot serve as an untouched confirmation of the general idea.
A genuinely prospective component can nevertheless be established:
1. use observations only through a locked cutoff date;
2. estimate the current tropical transformation vector;
3. predict subsequent monthly displacement, deformation, and terrestrial exposure;
4. compare those predictions with observations from the remainder of the event;
5. prohibit post hoc parameter adjustment before primary scoring.
The test would evaluate the model, not claim that ENSO itself was predicted by TSTOEAO.
17. Primary Prospective Predictions
17.1 Longitudinal ENSO prediction
During strengthening El Niño conditions, the fitted centroid of tropical Pacific convection and rainfall should move eastward relative to the neutral reference state.
The displacement should be visible in:
precipitation;
vertical motion;
cloud structure;
latent-heating proxies;
moisture convergence.
A precipitation-only displacement unsupported by circulation fields would be weaker evidence.
17.2 Opposite La Niña tendency
During La Niña conditions, the fitted tropical Pacific convective architecture should become more strongly west-centered relative to El Niño conditions.
The response need not be a perfect mirror.
17.3 ITCZ edge amplification
Regions near the climatological edge of the ITCZ should show larger precipitation sensitivity to a given latitudinal shift than regions near the broad maximum or well outside the rain belt.
Formally:
\[
\left|
\frac{\partial P}
{\partial\phi}
\right|
\uparrow
\Rightarrow
\left|
\Delta P
\right|
\uparrow
\]
for the same \(\Delta\phi\).
17.4 Basin-interception prediction
A transformation model fitted without basin-storage data should predict the sign of later river-flow or storage anomalies in basins whose exposure to the shifted moisture field changes substantially.
17.5 Topographic-switch prediction
Where a moisture corridor moves across a mountain or watershed divide, precipitation and runoff anomalies should change sharply across that boundary rather than vary only as smooth local amplitude changes.
17.6 Pulse-versus-storage prediction
Basins receiving concentrated short-duration precipitation should show lower durable storage efficiency than basins receiving comparable water totals over longer, infiltration-compatible periods, after controlling for soil, topography, and management.
17.7 Flood-on-drought prediction
Some regions experiencing flood peaks will retain negative long-duration storage anomalies because:
\[
P_{\mathrm{pulse}}
\not\Rightarrow
\Delta S_{\mathrm{durable}}>0.
\]
The template model should distinguish pulse delivery from persistent wet registration.
17.8 Persistence prediction
Long-term river, reservoir, groundwater, and terrestrial-water-storage anomalies should correlate more strongly with accumulated exposure to the transformed delivery field than with isolated extreme-rainfall events.
17.9 Transformation precedence
A measurable circulation or moisture-field displacement should precede or occur concurrently with the terrestrial precipitation anomaly.
The terrestrial result cannot consistently occur first if the proposed atmospheric route is causal.
17.10 Route-accounting prediction
When one region loses atmospheric moisture convergence, the broader moisture budget should reveal redistribution among:
altered vapor transport;
precipitation elsewhere;
atmospheric storage;
oceanic precipitation;
evaporation;
unresolved residual.
The prediction concerns constrained accounting, not an exact one-for-one geographic transfer.
18. Statistical Evaluation
18.1 Pattern correlation
Measure spatial agreement between predicted and observed fields.
18.2 Root-mean-square error
\[
\mathrm{RMSE}
=
\sqrt{
\frac{1}{N}
\sum_i
\left(
P_i^{\mathrm{obs}}
-
P_i^{\mathrm{pred}}
\right)^2
}.
\]
18.3 Explained variance
\[
R^2
=
1-
\frac{
\sum_i
\left(
P_i^{\mathrm{obs}}-P_i^{\mathrm{pred}}
\right)^2
}{
\sum_i
\left(
P_i^{\mathrm{obs}}-\bar P^{\mathrm{obs}}
\right)^2
}.
\]
18.4 Sign accuracy
Evaluate whether the model correctly predicts above-normal versus below-normal conditions.
18.5 Extreme-event skill
Assess:
hit rate;
false-alarm rate;
precision;
recall;
reliability;
probability calibration.
18.6 Transformation stability
A useful transformation parameter should not change radically when:
one dataset is replaced;
one region is omitted;
modest baseline changes are made;
one year is removed.
18.7 Complexity penalty
A deformable field can fit almost anything if unconstrained.
Model selection must penalize excessive degrees of freedom.
The more flexible model must produce genuine withheld predictive improvement.
19. Null and Alternative Models
19.1 Thermodynamic intensification
A warmer atmosphere can hold and transport more water vapor, potentially increasing heavy-precipitation intensity without requiring a major positional displacement. The IPCC assesses an intensifying water cycle, with increases in heavy precipitation in many regions and changes in drought and regional precipitation patterns.
19.2 Local land feedback
Soil moisture, vegetation, irrigation, urbanization, and land-cover change can alter precipitation and runoff locally.
19.3 Human water management
Reservoir operations, withdrawals, diversions, and groundwater pumping can dominate observed water levels independently of rainfall displacement.
19.4 Random internal variability
Some apparent wet-dry migration may arise from stochastic atmospheric variability rather than a coherent shifting architecture.
19.5 Stationary teleconnection indices
Established indices such as ENSO may predict anomalies without requiring explicit spherical registration.
The new model must demonstrate additional value.
19.6 Fully flexible prediction
A machine-learning system may predict precipitation more accurately while providing no simple shift interpretation.
The Shifted Hydrological Template gains value only if its interpretable parameters retain substantial predictive skill.
20. Failure Conditions
The hypothesis is weakened if:
1. rigid or deformable registration does not improve withheld prediction over amplitude-only models;
2. fitted shifts change sign or magnitude dramatically across credible datasets;
3. transformation parameters do not precede terrestrial anomalies;
4. the model succeeds only after seeing the target period or basin;
5. global rotation appears useful only because of excessive smoothing;
6. local intensity changes explain the same observations more simply;
7. apparent route transfer cannot be supported by atmospheric moisture-budget measurements;
8. basin storage changes are dominated by human operations not included in the model;
9. every failed prediction is explained by adding another unmeasured “knob” after the fact;
10. the unresolved residual grows systematically in the regions where the framework claims its strongest applicability;
11. a highly flexible displacement field reproduces observations but has no out-of-sample skill;
12. the model’s conclusions disappear when snow, evapotranspiration, or groundwater are included.
A framework that can always add another deformation after the outcome is not falsifiable.
21. Relationship to the Symmetry-Selected Spin-Route Experiment
The weather hypothesis and the WTe₂/Fe₃GaTe₂/hBN spin-route experiment occupy radically different scales and physical domains.
They nevertheless share a relational grammar.
Spin system
\[
\text{current orientation}
\ \text{relative to crystal symmetry}
\rightarrow
\text{spin-route selection}
\rightarrow
\text{magnetic expression}.
\]
Hydrological system
\[
\text{circulation orientation and position}
\ \text{relative to geography}
\rightarrow
\text{moisture-route interception}
\rightarrow
\text{hydrological expression}.
\]
In the spin system, rotating current relative to the crystal alters which spin-polarization route is symmetry-permitted.
In the hydrological system, shifting a rain belt, storm track, or moisture corridor relative to mountains and basins alters where water is intercepted and how it is expressed.
The common proposition is:
\[
\boxed{
\text{similar available capacity}
+
\text{changed relative alignment}
\rightarrow
\text{different realized route}
}
\]
The analogy must not be mistaken for identical mechanism.
Crystallographic symmetry imposes microscopic physical selection rules.
Atmospheric circulation and geography interact through fluid dynamics, thermodynamics, radiation, phase change, and topography.
The value lies in the shared experimental question:
> What changes when the relational alignment changes while other components remain as constant as the system permits?
22. Limits of the Shell Metaphor
The atmospheric layer is not rigid.
It does not rotate independently of Earth.
It is generated partly by the very surface over which it is registered.
The globe cannot be held experimentally constant while its entire atmospheric circulation is turned like a mechanical dial.
The metaphor therefore has strict limits.
The full reality includes:
\[
\text{translation}
+
\text{deformation}
+
\text{amplification}
+
\text{feedback}
+
\text{phase change}
+
\text{emergence}.
\]
The shell image remains valuable because it creates a disciplined first question:
> How much of the observed change resembles repositioning of an organized delivery field, and how much requires actual intensification, weakening, or structural transformation?
This distinction can be measured.
23. Engineering and Forecasting Implications
A successful transformation model could improve water planning by shifting attention from local rainfall forecasts alone to future basin exposure.
The relevant planning variables would include:
probability that a moisture corridor intersects the basin;
expected duration of intersection;
snow-versus-rain partition;
likely runoff efficiency;
groundwater-recharge probability;
reservoir-capture capacity;
flood-routing capacity;
persistence of dry-route exclusion.
Water infrastructure could then be designed around moving delivery pathways rather than stationary twentieth-century averages.
The engineering question becomes:
> Is the basin still positioned beneath the hydrological architecture for which its reservoirs, farms, cities, and groundwater assumptions were designed?
A city may not need less annual rainfall to become less secure.
It may need only:
later rainfall;
shorter rainfall;
more intense rainfall;
less snow;
greater evaporation;
repeated near-misses by storm corridors.
24. Broader TSTOEAO Implications
The Shifted Hydrological Template extends the TSTOEAO sequence from isolated objects toward relational field registration.
The decisive variable is not merely:
\[
E_{\mathrm{water}}.
\]
It is:
\[
Y_{\mathrm{water}}
=
\text{where the water pathway is}
\ \text{relative to where capture can occur}.
\]
The terrestrial result is therefore:
\[
V_{\mathrm{water}}
=
E_{\mathrm{moisture}}
\times
Y_{\mathrm{atmospheric\ route}}
\times
Y_{\mathrm{geographic\ interception}}
\times
Y_{\mathrm{surface\ retention}}.
\]
This expression is conceptual rather than a literal multiplication of independent scalars.
Its scientific value depends upon converting each term into measured fields and prospective predictions.
The paper’s principal methodological contribution is the proposed order of analysis:
\[
\boxed{
\text{map the delivery field}
\rightarrow
\text{register it to the globe}
\rightarrow
\text{estimate its movement}
\rightarrow
\text{measure geographic interception}
\rightarrow
\text{measure storage conversion}
\rightarrow
\text{preserve the residual}
}
\]
Conclusion
El Niño and La Niña demonstrate at the most accessible level that a major ocean-atmosphere pattern can shift the location of tropical convection and reorganize rainfall probabilities across the planet.
They show that:
continents need not move;
total planetary water need not change in direct proportion;
a changing circulation pattern can redirect where moisture rises, travels, condenses, and falls.
The same basic logic becomes more sophisticated when additional variables are introduced:
ITCZ latitude;
Walker-circulation longitude;
Hadley-cell width;
monsoon extent;
subtropical-high position;
jet-stream waviness;
storm-track location;
atmospheric-river landfall;
rainfall intensity;
system persistence;
seasonal phase;
freezing level;
soil condition;
basin architecture;
human water management.
The Earth can therefore be represented as a geographic sphere beneath a mobile and deformable hydrological template.
The representation is not literal machinery.
It is an observational and mathematical device.
The primary scientific question is:
> Can measured wet and dry anomalies be predicted by estimating how the atmospheric-hydrological field has shifted and deformed relative to the terrestrial surface?
The proposed answer must be earned through spherical registration, withheld prediction, basin-response testing, cross-dataset replication, physical moisture accounting, and explicit failure conditions.
The hypothesis is strengthened if:
stable displacement and deformation parameters emerge;
those parameters precede terrestrial anomalies;
basin exposure predicts river and storage response;
topographic and climatic boundaries amplify small shifts as predicted;
withheld regions and periods are forecast better than by simpler models.
It is weakened if:
local amplitude changes explain the observations more simply;
fitted transformations are unstable;
the method succeeds only retrospectively;
route redistribution cannot be measured;
residuals are concealed through unlimited post hoc complexity.
The deepest proposition is straightforward:
> A place may remain geographically fixed while its hydrological position changes.
A watershed can stay exactly where it has always been and nevertheless move, relationally, from beneath a dependable moisture pathway to its edge—or beyond it.
Another basin can move beneath a stronger path without moving at all.
The water did not simply become more or less.
The relationship changed.
And when the relationship changes, the realized world changes with it.
References
1. National Oceanic and Atmospheric Administration, Climate Prediction Center. “ENSO Diagnostic Discussion.” July 9, 2026.
2. National Oceanic and Atmospheric Administration. “What Is the El Niño–Southern Oscillation in a Nutshell?” NOAA Climate.gov.
3. National Oceanic and Atmospheric Administration. “El Niño and La Niña.” NOAA Climate.gov and National Ocean Service.
4. Guo, Y., et al. “Migration of the Intertropical Convergence Zone Driven by Ocean Circulation Changes.” Nature Communications 17 (2026). DOI: 10.1038/s41467-026-73200-2.
5. Kang, S. M., et al. “Extratropical Forcing and Tropical Rainfall Distribution: Energetics Framework and Ocean Ekman Advection.” npj Climate and Atmospheric Science 1 (2018). DOI: 10.1038/s41612-017-0004-6.
6. Intergovernmental Panel on Climate Change. “Water Cycle Changes.” In Climate Change 2021: The Physical Science Basis, Working Group I, Chapter 8. Cambridge University Press, 2021.
7. World Meteorological Organization. State of Global Water Resources 2024. Geneva: WMO, 2025.
8. Huang, H., et al. “State-of-the-Art Hydrological Datasets Exhibit Low Water-Balance Consistency.” Earth System Science Data 18 (2026): 3109–3124.
9. NASA Global Precipitation Measurement Mission. “IMERG: Integrated Multi-satellitE Retrievals for GPM.”
10. European Centre for Medium-Range Weather Forecasts. “ERA5: Fifth-Generation ECMWF Atmospheric Reanalysis.”
11. Rodell, M., Li, B., and Wiese, D. N. “Groundwater and Terrestrial Water Storage.” Bulletin of the American Meteorological Society 101, no. 8 (2020). DOI: 10.1175/BAMS-D-20-0104.1.
12. NASA and Jet Propulsion Laboratory. “Gravity Recovery and Climate Experiment Follow-On Mission.”
13. NASA. “SWOT Level 2 Lake Single-Pass Vector Data Product.”
14. NASA. “SWOT Level 2 River Single-Pass Vector Node Data Product.”
15. Wang, S., et al. “Extreme Atmospheric Rivers in a Warming Climate.” Nature Communications 14 (2023). DOI: 10.1038/s41467-023-38980-x.
16. Pan, M., et al. “Contrasting Historical Trends of Atmospheric Rivers in the Midlatitude Northern Hemisphere.” npj Climate and Atmospheric Science (2025). DOI: 10.1038/s41612-025-01191-w.
17. Dong, W., et al. “Opposing Trends in Winter Atmospheric Rivers over the Western and Eastern United States.” npj Climate and Atmospheric Science (2025). DOI: 10.1038/s41612-025-00998-x.
18. Denniston, R. F., et al. “Expansion and Contraction of the Indo-Pacific Tropical Rain Belt over the Last Three Millennia.” Scientific Reports 6 (2016): 34485. DOI: 10.1038/srep34485.
19. Huang, T., et al. “Equatorward Shift of the Boreal Summer Intertropical Convergence Zone over the Maritime Continent.” npj Climate and Atmospheric Science (2024). DOI: 10.1038/s41612-024-00593-6.
20. World Meteorological Organization. “From Drought to Deluge: WMO Report Highlights an Increasingly Erratic Water Cycle.” September 18, 2025.
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