Model Description

Theory & Mathematical Formulation

HydroRaVENS is a lumped, daily-timestep conceptual hydrological model. Water moves through three sequential processes each day: optional snowpack accumulation/melt, routing through cascading linear reservoirs, and evapotranspiration.

All fluxes are expressed as depths over the drainage basin (mm/day). Mass is conserved to within numerical precision.

Daily Water Balance

On each day, the model computes:

\[P + M - E = \Delta S + Q\]

where:

  • \(P\) = precipitation (mm/day)

  • \(M\) = snowmelt (mm/day)

  • \(E\) = evapotranspiration (mm/day)

  • \(\Delta S\) = change in storage (mm/day)

  • \(Q\) = streamflow (mm/day)

Snowpack Module (Optional)

If mean air temperature is provided, snowpack processes are enabled.

Accumulation:

When \(T \leq 0°C\), net water input (precipitation minus ET) accumulates as snow (stored as SWE):

\[\text{SWE}_{t+1} = \text{SWE}_t + (P_t - E_t)\]
Melt:

When \(T > 0°C\), melt is computed using the positive-degree-day (PDD) approach:

\[M_t = \min(\text{SWE}_t, \alpha \cdot T_t \cdot \Delta t)\]

where \(\alpha\) is the melt factor (mm SWE per °C per day).

All melt is routed directly to the top reservoir.

ET deficit:

When precipitation minus ET is negative, the deficit first sublimates snow:

\[\text{Sublimation} = \min\!\left(\text{SWE}_t,\ \max(0,\ E_t - P_t)\right)\]

Any deficit exceeding available SWE is passed to the top subsurface reservoir and, if still unmet, carried forward to the next time step.

Linear Reservoir Cascade

Water drains through a stack of reservoirs (top = shallowest, bottom = deepest). Each reservoir first receives its recharge input, then drains by exponential decay:

\[Q_i(t) = \bigl(H_i(t) + Q_{\text{recharge},i}\bigr) \cdot (1 - e^{-\Delta t / \tau_i})\]

where:

  • \(H_i\) = water depth in reservoir \(i\) at the start of the time step (m)

  • \(Q_{\text{recharge},i}\) = water input to reservoir \(i\) this time step (mm)

  • \(\tau_i\) = e-folding residence time (days)

  • \(\Delta t\) = time step (1 day)

Discharge Partitioning:

Of the water drained from reservoir \(i\), a fraction \(f_i\) exits as river discharge; the remainder infiltrates to the next layer:

\[\begin{split}Q_{\text{discharge},i} = f_i \cdot Q_i \\ Q_{\text{infiltrate},i} = (1 - f_i) \cdot Q_i\end{split}\]
Constraint:

The bottom reservoir should fully discharge (\(f_{\text{bottom}} = 1.0\)). A warning is issued if not, as this violates mass conservation.

Storage Update:

Recharge is applied first, then exponential drainage:

\[H_i(t+1) = \bigl(H_i(t) + Q_{\text{recharge},i}\bigr)\,e^{-\Delta t/\tau_i}\]

Overflow above \(H_{\max}\) exits immediately as direct runoff; any deficit is passed to the next-deeper reservoir. ET is not subtracted separately at the reservoir level — it is already incorporated into the recharge input to the top reservoir.

Evapotranspiration

Two methods are supported:

Method 1: From Data

ET is read directly from the input CSV and scaled to close the annual water balance:

\[E_{\text{scaled}} = E_{\text{observed}} \cdot \frac{P_{\text{annual}} - Q_{\text{observed,annual}}}{ET_{\text{observed,annual}}}\]
Method 2: Thornthwaite-Chang (2019)

Daily reference ET (\(ET_0\)) is estimated from temperature and photoperiod:

\[ET_0 = \text{f}(T_{\max}, T_{\min}, \text{photoperiod})\]

Then scaled by water year to match observed P − Q balance.

In both cases, the annual scaling factor is stored and applied to ensure that \(P - Q - E \approx 0\) on each water year.

Model Skill Evaluation

The Nash-Sutcliffe Efficiency (NSE) quantifies model performance:

\[\text{NSE} = 1 - \frac{\sum_t (Q_{\text{mod},t} - Q_{\text{obs},t})^2} {\sum_t (Q_{\text{obs},t} - \bar{Q}_{\text{obs}})^2}\]

  • \(\text{NSE} = 1\): Perfect simulation

  • \(\text{NSE} = 0\): Model performs as well as the observed mean

  • \(\text{NSE} < 0\): Model worse than using the mean as a predictor

Typical ranges:

  • \(\text{NSE} > 0.75\): Excellent

  • \(0.5 < \text{NSE} < 0.75\): Good

  • \(0.3 < \text{NSE} < 0.5\): Satisfactory

  • \(\text{NSE} < 0.3\): Poor

Model Assumptions & Limitations

Strengths:

  • ✅ Mass-conserving (exact balance)

  • ✅ Minimal data requirements (daily P and Q)

  • ✅ Fast computation (runs decades in seconds)

  • ✅ Physically interpretable parameters

  • ✅ Suitable for ungauged basins (transfer parameters)

Limitations:

  • ⚠️ Lumped model (no spatial variability)

  • ⚠️ Linear reservoirs (may not capture threshold behavior)

  • ⚠️ Daily timestep only (not suitable for event-scale analysis)

  • ⚠️ Simplified groundwater–surface-water interaction

  • ⚠️ Snowpack simplified (PDD model; ignores energy balance)

  • ⚠️ No representation of lakes or artificial storage

  • ⚠️ ET method choice matters; Thornthwaite-Chang is approximate

Best suited for:

  • Long-term water balance studies (years–decades)

  • Climate impact assessments

  • Ungauged or poorly-gauged basins

  • Parameter transfer to similar basins

  • Educational modeling