{ "metadata": { "name": "", "signature": "sha256:0c35b39584d7f14842e8294a8435ce58f31c0f8f3d8f1c934b0d98a47ee73920" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear reservoir\n", "This is a simple rainfall runoff model. Precipitation is randomly generated from an exponential distribution. Streamflow is governed by $\\frac{dS}{dt} = -kS$, where $S$ is the storage in the reservoir. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import sys\n", "sys.path.append('./../')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from stockflow import simulation\n", "import numpy as np\n", "from matplotlib import pyplot as plt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up the timestep vector and sample $P$ values. `t` should contain all the points where you want to evaluate the state variables; it is *not* necessarily where the ODE solver will sample. More on that in a bit." ] }, { "cell_type": "code", "collapsed": false, "input": [ "tmax = 100\n", "dt = 1\n", "t = np.arange(0,tmax,dt)\n", "P = 5*np.random.standard_exponential(len(t),)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously you'll want to pay attention to units here. This is just an example." ] }, { "cell_type": "code", "collapsed": false, "input": [ "k = 0.3" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now create the simulation object, create stocks with their initial conditions (in a dictionary), and create flows one by one with functions describing their behavior as a function of `t`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "s = simulation(t)\n", "s.stocks({'S': 0})\n", "\n", "# discrete forcing - use discrete=True keyword when calling s.run()\n", "s.flow('P', start=None, end='S', f=lambda t: P[t])\n", "s.flow('Q', start='S', end=None, f=lambda t: k*s.S)\n", "s.run(discrete=True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The functions can either be lambdas, or defined in the usual way with `def my_func(t): ...`. If you're using **discrete forcing data**, note that `P[t]` may be given index values `t` that are not integers. By default NumPy rounds these down to the nearest integer. This won't matter if your forcing is continuous in `t`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that the simulation is done, we can access all stock/flow timeseries using `s.Q` or `s.S`, for example. Let's plot streamflow." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(t, s.Q)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pretty easy. What does the output look like if we change $k$?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "k = 0.95\n", "s.run()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(t, s.Q)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see here the response is much more \"flashy\" with $k=0.95$ than with $k=0.3$ above. If we had the real $Q$ data we could compare them, calculate error, etc. " ] } ], "metadata": {} } ] }