{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Stommel — Two-Box Thermohaline Circulation Model\n", "\n", "**Author:** Jordan Landers \n", "**Date:** last-modified\n", "\n", "_Description:_ Temperature-salinity density contrast, overturning strength diagnostic, freshwater forcing (two attachment styles), thermally-driven vs salinity-driven bifurcation, time-varying parameters\n", "\n", "_Abstract_\n", "\n", "> `Stommel` models Atlantic overturning circulation as two boxes — equatorial and polar — exchanging heat and salinity driven by their density contrast. This notebook demonstrates freshwater perturbation via both parameter replacement and state-additive forcing, the bifurcation between thermally-driven and salinity-dominated overturning modes, and time-evolving parameter sweeps.\n", "\n", "**Keywords:** Stommel, thermohaline circulation, AMOC, overturning, freshwater forcing, bistability, salinity-driven mode, density contrast, bifurcation, register_forcing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "The Stommel (1961) model tracks two state variables — the pole-to-equator **temperature contrast** `T` and **salinity contrast** `S` — and uses them to compute an overturning circulation strength `q`. Both variables are dimensionless in the default parameter set.\n", "\n", "The diagnostic `q` is the key output: positive values indicate thermally-driven (on) circulation; negative values indicate haline-driven (reversed) circulation.\n", "\n", "### Equations\n", "\n", "$$\n", "q = k(\\alpha T - \\beta S)\n", "$$\n", "\n", "$$\n", "\\frac{dT}{dt} = -\\lambda_T (T - T^*) - |q|\\, T\n", "$$\n", "\n", "$$\n", "\\frac{dS}{dt} = E - \\lambda_S (S - S^*) - |q|\\, S\n", "$$\n", "\n", "The restoring terms pull `T` and `S` toward their equatorial references. The advective terms `|q|T` and `|q|S` represent overturning transport. `E` is a net freshwater flux (evaporation minus precipitation).\n", "\n", "### Parameters\n", "\n", "| Name | Description | Default |\n", "|------|-------------|---------|\n", "| `alpha` | Thermal expansion coefficient | 1.0 |\n", "| `beta` | Haline contraction coefficient | 1.0 |\n", "| `k` | Hydraulic constant (sensitivity of `q` to density contrast) | 1.0 |\n", "| `E` | Net evaporation-minus-precipitation freshwater flux | 0.0 |\n", "| `lambda_T` | Thermal restoring rate | 1.0 |\n", "| `lambda_S` | Saline restoring rate | 1.0 |\n", "| `T_star` | Equilibrium temperature contrast | 1.0 |\n", "| `S_star` | Equilibrium salinity contrast | 0.0 |\n", "\n", "All parameters accept a `float`, a callable `(t)` / `(t, state)`, or a `cc.Forcing` object. External forcings are attached after construction via `register_forcing` — see the Forcing section below.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic run" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import climatecritters as cc\n", "from climatecritters.model_critters.stommel import Stommel\n", "\n", "model = Stommel(E=0.3, T_star=1.0, S_star=0.0)\n", "output = model.integrate(t_span=(0, 50), y0=[1.0, 0.0], method='RK45')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "State variables and the overturning diagnostic are accessed directly from the output object:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T = output.state_variables['T']\n", "S = output.state_variables['S']\n", "q = output.diagnostic_variables['q']\n", "time = output.time\n", "\n", "fig, axes = plt.subplots(3, 1, figsize=(8, 7), sharex=True)\n", "axes[0].plot(time, T, color='firebrick'); axes[0].set_ylabel('T')\n", "axes[1].plot(time, S, color='steelblue'); axes[1].set_ylabel('S')\n", "axes[2].plot(time, q, color='purple')\n", "axes[2].axhline(0, color='k', lw=0.8, ls='--')\n", "axes[2].set_ylabel('q (overturning)'); axes[2].set_xlabel('time')\n", "fig.suptitle('Stommel — E=0.3'); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Figure.** Default run ($E=0.3$, $T^*=1$). Temperature contrast $T$ equilibrates quickly (fast restoring). Salinity contrast $S$ evolves more slowly under the specified freshwater exchange. Overturning $q$ starts positive (temperature-driven, TH mode) and settles to a steady value — the system remains in the thermally-direct circulation state for these parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Forcing\n", "\n", "Forcings are attached after construction using `register_forcing`. There are two meaningfully different places to attach a freshwater forcing in this model, with different physical interpretations.\n", "\n", "First, build the forcing object. `cc.Forcing` accepts a callable, an array with a time axis, or a sequence of composable `Hold`, `Ramp`, and `Harmonic` elements:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "fw_forcing = cc.Forcing.from_sequence([\n", " cc.forcing.Hold(duration=10, value=0.0),\n", " cc.forcing.Ramp(duration=5, y0=0.0, yf=0.5),\n", " cc.forcing.Hold(duration=15, value=0.5),\n", " cc.forcing.Ramp(duration=5, y0=0.5, yf=0.0),\n", " cc.forcing.Hold(duration=15, value=0.0),\n", "])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Always plot the forcing first so the signal is explicit before running any model:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_plot = np.linspace(0, 50, 500)\n", "fig, ax = plt.subplots(figsize=(8, 2.5))\n", "ax.plot(t_plot, [fw_forcing.get_forcing(t) for t in t_plot], color='teal')\n", "ax.set_xlabel('time'); ax.set_ylabel('freshwater flux'); ax.set_title('Freshwater pulse forcing')\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Approach 1: parameter replacement on `E`\n", "\n", "`register_forcing('E', forcing_obj)` replaces the `E` parameter entirely with the forcing value at each timestep. This is the natural physical interpretation: the forcing *is* the freshwater flux. Any value of `E` set at construction is overridden during integration." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "m_E = Stommel(E=0.0, T_star=1.0, S_star=0.0)\n", "m_E.register_forcing('E', fw_forcing) # attachment_style='replacement', timing='pre' by default\n", "out_E = m_E.integrate(t_span=(0, 50), y0=[1.0, 0.0], method='RK45')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Approach 2: additive forcing on state variable `S`\n", "\n", "`register_forcing('S', forcing_obj, 'additive', timing='pre')` adds the forcing value to `dS/dt` inside the right-hand side at each function evaluation. This is a perturbation on top of whatever `E` is already doing." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "m_S = Stommel(E=0.0, T_star=1.0, S_star=0.0)\n", "m_S.register_forcing('S', fw_forcing, 'additive', timing='pre')\n", "out_S = m_S.integrate(t_span=(0, 50), y0=[1.0, 0.0], method='RK45')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparing the two approaches\n", "\n", "When `E=0` at construction, both approaches are **mathematically equivalent**: replacing `E` with `F(t)` gives `dS/dt = F(t) - ...`, and adding `F(t)` to `dS/dt` with `E=0` gives the same expression." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_plot = np.linspace(0, 50, 500)\n", "\n", "fig, axes = plt.subplots(3, 1, figsize=(9, 8), sharex=True)\n", "\n", "axes[0].plot(t_plot, [fw_forcing.get_forcing(t) for t in t_plot], color='teal')\n", "axes[0].set_ylabel('forcing value'); axes[0].set_title('Applied freshwater signal')\n", "\n", "axes[1].plot(out_E.time, out_E.diagnostic_variables['q'],\n", " color='purple', lw=2, label='E replacement (E=0 base)')\n", "axes[1].plot(out_S.time, out_S.diagnostic_variables['q'],\n", " color='orange', lw=1.5, ls='--', label='S additive pre (E=0 base)')\n", "axes[1].axhline(0, color='k', lw=0.8, ls=':')\n", "axes[1].set_ylabel('q (overturning)'); axes[1].legend(fontsize=9)\n", "\n", "axes[2].plot(out_E.time, out_E.state_variables['S'],\n", " color='steelblue', lw=2, label='E replacement')\n", "axes[2].plot(out_S.time, out_S.state_variables['S'],\n", " color='coral', lw=1.5, ls='--', label='S additive pre')\n", "axes[2].set_ylabel('S'); axes[2].set_xlabel('time'); axes[2].legend(fontsize=9)\n", "\n", "fig.suptitle('E=0 baseline: both approaches are equivalent', y=1.01)\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Figure.** With $E=0$ at construction, both forcing approaches are equivalent: the overturning $q$ traces are indistinguishable (top panel for E-replacement, overlapping dashes for S-additive). The freshwater pulse briefly weakens overturning; the system recovers when the pulse ends. The forcing itself is shown in the top panel for reference." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The distinction matters when there is a non-zero baseline `E`. **Parameter replacement** overrides the baseline entirely during the forced period. **Additive pre-step** superposes the forcing on top of it:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# E=0.3 baseline — replacement overrides it; additive adds on top\n", "m_E_base = Stommel(E=0.3, T_star=1.0, S_star=0.0)\n", "m_E_base.register_forcing('E', fw_forcing) # E(t) = fw_forcing, ignoring 0.3\n", "\n", "m_S_base = Stommel(E=0.3, T_star=1.0, S_star=0.0)\n", "m_S_base.register_forcing('S', fw_forcing, 'additive', timing='pre') # dS/dt gets +fw_forcing ON TOP of E=0.3\n", "\n", "out_E_base = m_E_base.integrate(t_span=(0, 50), y0=[1.0, 0.0], method='RK45')\n", "out_S_base = m_S_base.integrate(t_span=(0, 50), y0=[1.0, 0.0], method='RK45')\n", "\n", "fig, ax = plt.subplots(figsize=(8, 4))\n", "ax.plot(output.time, output.diagnostic_variables['q'],\n", " color='gray', ls='--', label='unforced (E=0.3)')\n", "ax.plot(out_E_base.time, out_E_base.diagnostic_variables['q'],\n", " color='purple', label='E replacement (forcing replaces E=0.3)')\n", "ax.plot(out_S_base.time, out_S_base.diagnostic_variables['q'],\n", " color='orange', label='S additive pre (forcing + E=0.3)')\n", "ax.axhline(0, color='k', lw=0.8, ls=':')\n", "ax.set_ylabel('q (overturning)'); ax.set_xlabel('time'); ax.legend(fontsize=9)\n", "ax.set_title('Non-zero baseline: replacement vs. additive diverge')\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Figure.** With $E=0.3$ at construction, the two approaches diverge. E-replacement: the baseline $E=0.3$ is completely overridden — during Hold periods `E=0`, so the effective freshwater input is zero. S-additive: the forcing adds on top of the existing $E=0.3$ term in $\\dot{S}$, so the total freshwater influence is $E + f(t)$. Choose the approach that matches the physical interpretation of your forcing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Summary of the two approaches:**\n", "\n", "| | `register_forcing('E', ...)` | `register_forcing('S', ..., 'additive', timing='pre')` |\n", "|--|--|--|\n", "| Acts on | parameter `E` in `param_values` | state variable `S` via `dS/dt` |\n", "| With non-zero `E` | replaces the baseline entirely | adds perturbation on top of baseline |\n", "| Physical meaning | the forcing *is* the net freshwater flux | an additional flux injected into the salinity budget |\n", "| With adaptive solver (RK45) | ✓ applied at every function evaluation | ✓ applied at every function evaluation |\n", "\n", "> **Note on `timing='post'`:** Registering a state-variable additive forcing with `timing='post'` would add the forcing value directly to `S` after each integration step (rather than to `dS/dt`). This is not physically meaningful here and will generate a warning when used with adaptive solvers, which do not support post-step application.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Time-evolving parameters\n", "\n", "Any parameter in `param_values` can be a callable instead of a scalar. The dispatcher accepts `(t)`, `(t, state)`, or `(t, state, model)`. Here `E` drifts upward slowly without using a `Forcing` object:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def E_ramp(t):\n", " return np.clip(0.012 * t, 0.0, 0.6)\n", "\n", "model_ramp = Stommel(E=E_ramp, T_star=1.0, S_star=0.0)\n", "out_ramp = model_ramp.integrate(t_span=(0, 50), y0=[1.0, 0.0], method='RK45')\n", "\n", "fig, axes = plt.subplots(2, 1, figsize=(8, 5), sharex=True)\n", "axes[0].plot(out_ramp.time, out_ramp.diagnostic_variables['q'], color='purple')\n", "axes[0].axhline(0, color='k', lw=0.8, ls='--'); axes[0].set_ylabel('q')\n", "t_plot = np.linspace(0, 50, 500)\n", "axes[1].plot(t_plot, [E_ramp(t) for t in t_plot], color='teal')\n", "axes[1].set_ylabel('E(t)'); axes[1].set_xlabel('time')\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Figure.** Top: overturning $q$ under a linearly increasing $E$ (freshwater input). $q$ declines steadily and crosses zero around $t \\approx 35$ — the circulation collapses from thermally-direct (TH mode, $q>0$) to salinity-driven (SA mode, $q<0$). Bottom: the $E(t)$ ramp used. This is the canonical Stommel bifurcation: once $q<0$, the system is in a different stable state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Converting to pyleoclim" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "{}\n" ] } ], "source": [ "ts_q = output.to_pyleo(var_names=['q'])\n", "ts_q.plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solver notes\n", "\n", "RK45 is appropriate for this model. Near an overturning collapse (where `q` passes through zero) the system can stiffen — tighten tolerances if trajectories look erratic:\n", "\n", "```python\n", "output = model.integrate(\n", " t_span=(0, 50), y0=[1.0, 0.0], method='RK45',\n", " kwargs={'rtol': 1e-8, 'atol': 1e-10},\n", ")\n", "```\n", "\n", "The diagnostic `q` is computed from the full trajectory *after* integration (`uses_post_history = True`) and is not available mid-run." ] } ], "metadata": { "kernelspec": { "display_name": "pb_env_jpl", "language": "python", "name": "pb_env_jpl", "path": "/Users/jlanders/Library/Jupyter/kernels/pb_env_jpl" }, "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 4 }