Regression Curves for Total Suspended Sediment and Sand.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Objectives\n",
    "\n",
    "- Generate scatter plots and regression curves for total suspended sediment and suspended sand concentration. \n",
    "- Convert concentrations to loads and repeat regression analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.) Select site and check that ten years of data is available\n",
    "\n",
    "USGS Site Identifier: 7381495 \n",
    "Location: Atchafalaya River at Melville, LA\n",
    "\n",
    "First I looked at the comments (turning off for saving this notebook):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!head -n 53 discrete_data.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The column headers start at line 52, so I'll read in the data frame from there:\n",
    "\n",
    "cek: we could do this so we get directly from the web"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas\n",
    "f = pandas.read_csv(\"discrete_data.csv\",header=52)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The time period covered is about 40 years:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('1979-11-09 13:00:00', '2019-06-20 11:00:00')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(f.DATETIME[0],f.DATETIME[410])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SITE_NO</th>\n",
       "      <th>STATION_NM</th>\n",
       "      <th>DATETIME</th>\n",
       "      <th>DCOMMENT</th>\n",
       "      <th>ICOMMENT</th>\n",
       "      <th>SSC</th>\n",
       "      <th>DAILYFLOW</th>\n",
       "      <th>INSTFLOW</th>\n",
       "      <th>GH</th>\n",
       "      <th>P2</th>\n",
       "      <th>...</th>\n",
       "      <th>TURB63680</th>\n",
       "      <th>TEMPC</th>\n",
       "      <th>TEMPAIRC</th>\n",
       "      <th>SC</th>\n",
       "      <th>SCLAB</th>\n",
       "      <th>DSS</th>\n",
       "      <th>PH</th>\n",
       "      <th>PHLAB</th>\n",
       "      <th>END_DATE</th>\n",
       "      <th>END_TIME</th>\n",
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       "      <th>0</th>\n",
       "      <td>7381495</td>\n",
       "      <td>(COE) Atchafalaya River at Melville, LA</td>\n",
       "      <td>1979-11-09 13:00:00</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>470.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <th>1</th>\n",
       "      <td>7381495</td>\n",
       "      <td>(COE) Atchafalaya River at Melville, LA</td>\n",
       "      <td>1979-12-14 15:00:00</td>\n",
       "      <td>S</td>\n",
       "      <td>S</td>\n",
       "      <td>224</td>\n",
       "      <td>281000.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>298.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7381495</td>\n",
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       "      <td>1980-01-25 09:30:00</td>\n",
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       "      <td>264</td>\n",
       "      <td>225000.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>281.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7381495</td>\n",
       "      <td>(COE) Atchafalaya River at Melville, LA</td>\n",
       "      <td>1980-02-07 09:30:00</td>\n",
       "      <td>S</td>\n",
       "      <td>S</td>\n",
       "      <td>235</td>\n",
       "      <td>191000.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.5</td>\n",
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       "      <td>276.0</td>\n",
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       "      <td>7.3</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>7381495</td>\n",
       "      <td>(COE) Atchafalaya River at Melville, LA</td>\n",
       "      <td>1980-03-12 13:00:00</td>\n",
       "      <td>S</td>\n",
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       "      <td>166</td>\n",
       "      <td>151000.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>10.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>408.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "<p>5 rows × 45 columns</p>\n",
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      "text/plain": [
       "   SITE_NO                               STATION_NM             DATETIME  \\\n",
       "0  7381495  (COE) Atchafalaya River at Melville, LA  1979-11-09 13:00:00   \n",
       "1  7381495  (COE) Atchafalaya River at Melville, LA  1979-12-14 15:00:00   \n",
       "2  7381495  (COE) Atchafalaya River at Melville, LA  1980-01-25 09:30:00   \n",
       "3  7381495  (COE) Atchafalaya River at Melville, LA  1980-02-07 09:30:00   \n",
       "4  7381495  (COE) Atchafalaya River at Melville, LA  1980-03-12 13:00:00   \n",
       "\n",
       "  DCOMMENT ICOMMENT  SSC  DAILYFLOW  INSTFLOW  GH  P2  ...  TURB63680  TEMPC  \\\n",
       "0        S        S  200   114000.0       NaN NaN NaN  ...        NaN   16.0   \n",
       "1        S        S  224   281000.0       NaN NaN NaN  ...        NaN    NaN   \n",
       "2        S        S  264   225000.0       NaN NaN NaN  ...        NaN    9.5   \n",
       "3        S        S  235   191000.0       NaN NaN NaN  ...        NaN    5.5   \n",
       "4        S        S  166   151000.0       NaN NaN NaN  ...        NaN   10.5   \n",
       "\n",
       "   TEMPAIRC     SC  SCLAB  DSS   PH  PHLAB  END_DATE  END_TIME  \n",
       "0       NaN  470.0    NaN  NaN  7.2    NaN       NaN       NaN  \n",
       "1       NaN  298.0    NaN  NaN  7.0    NaN       NaN       NaN  \n",
       "2       NaN  281.0    NaN  NaN  6.4    NaN       NaN       NaN  \n",
       "3       NaN  276.0    NaN  NaN  7.3    NaN       NaN       NaN  \n",
       "4       NaN  408.0    NaN  NaN  7.7    NaN       NaN       NaN  \n",
       "\n",
       "[5 rows x 45 columns]"
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   "source": [
    "f.head()"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First compare instantenous and daily flow record."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from IPython.display import set_matplotlib_formats\n",
    "%matplotlib inline\n",
    "set_matplotlib_formats('svg')\n",
    "f.DATETIME = pandas.to_datetime(f.DATETIME)\n",
    "plt.figure()\n",
    "plt.plot(f.DATETIME,f.DAILYFLOW,f.DATETIME,f.INSTFLOW)\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('Discharge [cfs]')\n",
    "plt.title('Flow Record')\n",
    "plt.legend(['Daily','Instantaneous']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The daily and instantaneous flow values don't overlap, so I'll just combine them.\n",
    "\n",
    "Also, there is missing data included as NaN's, so I'll filter those out and go ahead and calculate fines as\n",
    "`ssc*p63/100` and sand as `ssc*(1-p63/100)` while I'm at it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "flow=[]\n",
    "ssc=[]\n",
    "flowfine=[]\n",
    "fine=[]\n",
    "sand=[]\n",
    "for i, (daily, inst, p63) in enumerate(zip(f.DAILYFLOW,f.INSTFLOW, f.P63)):\n",
    "    hasData=True\n",
    "    if np.isnan(daily):\n",
    "        if not np.isnan(inst):\n",
    "            flow.append(inst)\n",
    "            ssc.append(f.SSC[i])\n",
    "        else:\n",
    "            hasData=False\n",
    "    else:\n",
    "        flow.append(daily)\n",
    "        ssc.append(f.SSC[i])\n",
    "    if hasData and not np.isnan(p63):\n",
    "        flowfine.append(flow[-1])\n",
    "        fine.append(ssc[-1]*p63/100.0)\n",
    "        sand.append(ssc[-1]*(1.-p63/100.0))\n",
    "flow = np.array(flow)\n",
    "ssc = np.array(ssc)\n",
    "flowfine=np.array(flowfine)\n",
    "fine=np.array(fine)\n",
    "sand=np.array(sand)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now plot and do linear and power regression on the total, fine, and sand concentrations \n",
    "\n",
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>slopes</th>\n",
       "      <th>intercepts</th>\n",
       "      <th>r_value</th>\n",
       "      <th>p_value</th>\n",
       "      <th>std err</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SSC</th>\n",
       "      <td>0.000356</td>\n",
       "      <td>103.633200</td>\n",
       "      <td>0.321079</td>\n",
       "      <td>4.819010e-11</td>\n",
       "      <td>0.000053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fines</th>\n",
       "      <td>0.000106</td>\n",
       "      <td>127.913052</td>\n",
       "      <td>0.113719</td>\n",
       "      <td>2.344843e-02</td>\n",
       "      <td>0.000047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sand</th>\n",
       "      <td>0.000264</td>\n",
       "      <td>-27.614932</td>\n",
       "      <td>0.721982</td>\n",
       "      <td>3.663475e-65</td>\n",
       "      <td>0.000013</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         slopes  intercepts   r_value       p_value   std err\n",
       "SSC    0.000356  103.633200  0.321079  4.819010e-11  0.000053\n",
       "Fines  0.000106  127.913052  0.113719  2.344843e-02  0.000047\n",
       "Sand   0.000264  -27.614932  0.721982  3.663475e-65  0.000013"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "ssc_lin = stats.linregress(x=flow,y=ssc)\n",
    "fine_lin = stats.linregress(x=flowfine,y=fine)\n",
    "sand_lin = stats.linregress(x=flowfine,y=sand)\n",
    "lin = pandas.DataFrame([ssc_lin,fine_lin,sand_lin], \n",
    "                       columns=[\"slopes\", \n",
    "                          \"intercepts\", \n",
    "                          \"r_value\", \n",
    "                          \"p_value\", \n",
    "                          \"std err\"],\n",
    "                       index=['SSC','Fines','Sand'])\n",
    "lin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "plt.scatter(flow,ssc)\n",
    "plt.scatter(flowfine,fine)\n",
    "plt.scatter(flowfine,sand)\n",
    "plt.plot(flow,ssc_lin[1]+ssc_lin[0]*flow,'r')\n",
    "plt.plot(flowfine,fine_lin[1]+fine_lin[0]*flowfine,'g')\n",
    "plt.plot(flowfine,sand_lin[1]+sand_lin[0]*flowfine,'b')\n",
    "plt.legend(['Total','Fine','Sand'])\n",
    "plt.xlabel('Discharge [cfs]')\n",
    "plt.title('Suspended Sediment vs. Discharge')\n",
    "plt.ylabel('Sediment Concentration [mg/l]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Power Law Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>slopes</th>\n",
       "      <th>intercepts</th>\n",
       "      <th>r_value</th>\n",
       "      <th>p_value</th>\n",
       "      <th>std err</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SSC</th>\n",
       "      <td>0.734762</td>\n",
       "      <td>-4.001486</td>\n",
       "      <td>0.586917</td>\n",
       "      <td>2.152241e-38</td>\n",
       "      <td>0.050807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fines</th>\n",
       "      <td>0.435611</td>\n",
       "      <td>-0.539711</td>\n",
       "      <td>0.365857</td>\n",
       "      <td>5.102157e-14</td>\n",
       "      <td>0.055755</td>\n",
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       "      <th>Sand</th>\n",
       "      <td>2.505807</td>\n",
       "      <td>-28.139084</td>\n",
       "      <td>0.834290</td>\n",
       "      <td>2.446685e-101</td>\n",
       "      <td>0.084503</td>\n",
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      ],
      "text/plain": [
       "         slopes  intercepts   r_value        p_value   std err\n",
       "SSC    0.734762   -4.001486  0.586917   2.152241e-38  0.050807\n",
       "Fines  0.435611   -0.539711  0.365857   5.102157e-14  0.055755\n",
       "Sand   2.505807  -28.139084  0.834290  2.446685e-101  0.084503"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "log_flow = np.log(flow)\n",
    "log_flowfine = np.log(flowfine)\n",
    "log_ssc = np.log(ssc)\n",
    "log_fine = np.log(fine)\n",
    "sand_indeces = np.where(sand > 0.0)\n",
    "log_flowfine_sand = np.log(flowfine[sand_indeces])\n",
    "log_sand = np.log(sand[sand_indeces])\n",
    "ssc_pow = stats.linregress(x=log_flow,y=log_ssc)\n",
    "fine_pow = stats.linregress(x=log_flowfine,y=log_fine)\n",
    "sand_pow = stats.linregress(x=log_flowfine_sand,y=log_sand)\n",
    "pow = pandas.DataFrame([ssc_pow,fine_pow,sand_pow], \n",
    "                       columns=[\"slopes\", \n",
    "                          \"intercepts\", \n",
    "                          \"r_value\", \n",
    "                          \"p_value\", \n",
    "                          \"std err\"],\n",
    "                       index=['SSC','Fines','Sand'])\n",
    "pow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
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   ],
   "source": [
    "import math\n",
    "plt.scatter(log_flow,log_ssc,c='r')\n",
    "plt.scatter(log_flowfine,log_fine,c='g')\n",
    "plt.scatter(log_flowfine_sand,log_sand,c='b')\n",
    "plt.plot(log_flow,ssc_pow[1]+ssc_pow[0]*log_flow,'r')\n",
    "plt.plot(log_flowfine,fine_pow[1]+fine_pow[0]*log_flowfine,'g')\n",
    "plt.plot(log_flowfine_sand,sand_pow[1]+sand_pow[0]*log_flowfine_sand,'b')\n",
    "plt.legend(['Total','Fine','Sand'])\n",
    "plt.title('Suspended Sediment vs. Discharge')\n",
    "plt.xlabel('Discharge [log(cfs)]')\n",
    "plt.ylabel('Sediment Concentration [log(mg/l)]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sediment Load\n",
    "\n",
    "Sediment load is the sediment discharge (product of water discharge and concentration.\n",
    "\n",
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>slopes</th>\n",
       "      <th>intercepts</th>\n",
       "      <th>r_value</th>\n",
       "      <th>p_value</th>\n",
       "      <th>std err</th>\n",
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       "      <th>SSC Load</th>\n",
       "      <td>0.712903</td>\n",
       "      <td>-31173.342117</td>\n",
       "      <td>0.673341</td>\n",
       "      <td>3.718344e-54</td>\n",
       "      <td>0.039237</td>\n",
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       "    <tr>\n",
       "      <th>Fines Load</th>\n",
       "      <td>0.372013</td>\n",
       "      <td>16377.957448</td>\n",
       "      <td>0.485260</td>\n",
       "      <td>7.646737e-25</td>\n",
       "      <td>0.033727</td>\n",
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       "      <th>Sand Load</th>\n",
       "      <td>0.352196</td>\n",
       "      <td>-49950.466045</td>\n",
       "      <td>0.791032</td>\n",
       "      <td>2.558973e-86</td>\n",
       "      <td>0.013705</td>\n",
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      "text/plain": [
       "              slopes    intercepts   r_value       p_value   std err\n",
       "SSC Load    0.712903 -31173.342117  0.673341  3.718344e-54  0.039237\n",
       "Fines Load  0.372013  16377.957448  0.485260  7.646737e-25  0.033727\n",
       "Sand Load   0.352196 -49950.466045  0.791032  2.558973e-86  0.013705"
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     "execution_count": 25,
     "metadata": {},
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   "source": [
    "K=.0027 #conversion factor to get Q_s from discharge and concentration in mg/l\n",
    "q_total = flow*ssc*K\n",
    "q_fine = flowfine*fine*K\n",
    "q_sand = flowfine*sand*K\n",
    "q_total_lin = stats.linregress(x=flow,y=q_total)\n",
    "q_fine_lin = stats.linregress(x=flowfine,y=q_fine)\n",
    "q_sand_lin = stats.linregress(x=flowfine,y=q_sand)\n",
    "q_lin = pandas.DataFrame([q_total_lin,q_fine_lin,q_sand_lin], \n",
    "                       columns=[\"slopes\", \n",
    "                          \"intercepts\", \n",
    "                          \"r_value\", \n",
    "                          \"p_value\", \n",
    "                          \"std err\"],\n",
    "                       index=['SSC Load','Fines Load','Sand Load'])\n",
    "q_lin"
   ]
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  {
   "cell_type": "code",
   "execution_count": 26,
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   ],
   "source": [
    "plt.scatter(flow,q_total,c='r')\n",
    "plt.scatter(flowfine,q_fine,c='g')\n",
    "plt.scatter(flowfine,q_sand,c='b')\n",
    "plt.plot(flow,q_total_lin[1]+q_total_lin[0]*flow,'r')\n",
    "plt.plot(flowfine,q_fine_lin[1]+q_sand_lin[0]*flowfine,'g')\n",
    "plt.plot(flowfine,q_sand_lin[1]+q_sand_lin[0]*flowfine,'b')\n",
    "plt.legend(['Total','Fine','Sand']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Power Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>slopes</th>\n",
       "      <th>intercepts</th>\n",
       "      <th>r_value</th>\n",
       "      <th>p_value</th>\n",
       "      <th>std err</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Total Load</th>\n",
       "      <td>1.734762</td>\n",
       "      <td>-9.915989</td>\n",
       "      <td>0.863420</td>\n",
       "      <td>2.505447e-120</td>\n",
       "      <td>0.050807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fines Load</th>\n",
       "      <td>1.435611</td>\n",
       "      <td>-6.454214</td>\n",
       "      <td>0.791611</td>\n",
       "      <td>1.575747e-86</td>\n",
       "      <td>0.055755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sand Load</th>\n",
       "      <td>2.505807</td>\n",
       "      <td>-28.139084</td>\n",
       "      <td>0.834290</td>\n",
       "      <td>2.446685e-101</td>\n",
       "      <td>0.084503</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              slopes  intercepts   r_value        p_value   std err\n",
       "Total Load  1.734762   -9.915989  0.863420  2.505447e-120  0.050807\n",
       "Fines Load  1.435611   -6.454214  0.791611   1.575747e-86  0.055755\n",
       "Sand Load   2.505807  -28.139084  0.834290  2.446685e-101  0.084503"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "log_flow = np.log(flow)\n",
    "log_flowfine = np.log(flowfine)\n",
    "log_q_total = np.log(q_total)\n",
    "log_q_fine = np.log(q_fine)\n",
    "q_sand_indeces = np.where(q_sand > 0.0)\n",
    "log_flowfine_q_sand = np.log(flowfine[q_sand_indeces])\n",
    "log_q_sand = np.log(sand[q_sand_indeces])\n",
    "q_total_pow = stats.linregress(x=log_flow,y=log_q_total)\n",
    "q_fine_pow = stats.linregress(x=log_flowfine,y=log_q_fine)\n",
    "q_sand_pow = stats.linregress(x=log_flowfine_sand,y=log_q_sand)\n",
    "pow = pandas.DataFrame([q_total_pow,q_fine_pow,q_sand_pow], \n",
    "                       columns=[\"slopes\", \n",
    "                          \"intercepts\", \n",
    "                          \"r_value\", \n",
    "                          \"p_value\", \n",
    "                          \"std err\"],\n",
    "                       index=['Total Load','Fines Load','Sand Load'])\n",
    "pow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
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   "source": [
    "plt.scatter(log_flow,log_q_total,c='r')\n",
    "plt.scatter(log_flowfine,log_q_fine,c='g')\n",
    "plt.scatter(log_flowfine_sand,log_q_sand,c='b')\n",
    "plt.plot(log_flow,q_total_pow[1]+q_total_pow[0]*log_flow,'r')\n",
    "plt.plot(log_flowfine,q_fine_pow[1]+q_fine_pow[0]*log_flowfine,'g')\n",
    "plt.plot(log_flowfine_sand,q_sand_pow[1]+q_sand_pow[0]*log_flowfine_sand,'b')\n",
    "plt.legend(['Total','Fine','Sand'])\n",
    "plt.xlabel('log(cfs)')\n",
    "plt.ylabel('log(mg/l)');"
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