SnowMelting

This repository contains the SnowMelting component of the GEOframe modeling framework, implemented in Java. It provides various conceptual models for simulating snow dynamics, primarily focusing on Snow Water Equivalent (SWE) and snowmelt processes.

Point-Case

The core models are implemented within the it.geoframe.blogspot.snowmelting.pointcase package and are designed for single-point simulations.

This component currently includes three primary snowmelt models:

• SnowMeltingPointCaseCazorzi.java: Implements the Cazorzi snowmelt model (Specifics TODO: Add details on the Cazorzi model formulation).

• SnowMeltingPointCaseDegreeDay.java: Implements the Temperature Index (Degree-Day) method.

• SnowMeltingPointCaseHock.java: Implements the Hock snowmelt model (Specifics TODO: Add details on the Hock model formulation).

Raster-Case Implementation

TODO: Tdocumentations for classes for raster-based ( in it.geoframe.blogspot.snowmelting.rastercase), .

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Mathematical Formulation: Temperature Index Method

The Degree-Day model (SnowMeltingPointCaseDegreeDay.java) is based on the classical temperature index method, as described in Formetta et al. (2014).

Snowmelt and freezing model (temperature index method; Formetta et al., 2014)

$$ \begin{aligned} L_{\max}(t) &= \alpha_l, S_w(t) \\ \frac{dS_w(t)}{dt} &= P_s(t) + F(t) - M(t) \\ \frac{dL_w(t)}{dt} &= P_r(t) - F(t) + M(t) \end{aligned} $$

Solid and liquid water dynamics

$$ \begin{aligned} M_d(t) &= \max\left(0,; L(t) - L_{\max}(t)\right) \\ L_w(t) &= \min\left(L(t),; L_{\max}(t)\right) \\ SWE(t) &= S_w(t) + L_w(t) \end{aligned} $$

Snow Water Equivalent — Symbols Table

Symbol	Meaning	Dimension
$$P(t)$$	Precipitation at time t	[L·T⁻¹]
$$P_r(t)$$	Rainfall at time t	[L·T⁻¹]
$$P_s(t)$$	Snowfall at time t	[L·T⁻¹]
$$T$$	Temperature	[Θ]
$$T_s$$	Threshold air temperature	[Θ]
$$α_m$$	Melt factor	[L·T⁻¹·Θ⁻¹]
$$α_f$$	Freezing factor	[L·T⁻¹·Θ⁻¹]
$$α_l$$	Coefficient for maximum liquid water	–
$$M(t)$$	Melt rate at time t	[L·T⁻¹]
$$F(t)$$	Freezing rate at time t	[L·T⁻¹]
$$S_w(t)$$	Solid water	[L]
$$L_w(t)$$	Liquid water	[L]
$$L_max(t)$$	Maximum liquid water value	[L]
$$SWE(t)$$	Snow Water Equivalent	[L]

Symbol	Meaning	Examples
L	Length	mm, m, km, water depth, elevation
T	Time	seconds, hours, days
M	Mass	kg
Θ	Thermodynamic temperature	°C, K
–	Dimensionless quantity	coefficients, ratios, fractions

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References

TODO: add all references

Formetta, G., Kampf, S. K., David, O., & Rigon, R. (2014, 6 May). Snow water equivalent modeling components in NewAge-JGrass. Geosci. Model Dev., 7 (3), 725–736.