FAO Meteorology Equations (#168)

Author: cyschneck

ncl/ncl_entries/meteorology.ipynb

@@ -27,7 +27,15 @@
    "metadata": {},
    "source": [
     "## dewtemp_trh\n",
-    "NCL's `dewtemp_trh` calculates the dew point temperature given temperature and relative humidity using the equations from John Dutton's _\"Ceaseless Wind\"_ (pg. 273-274){footcite}`dutton_1986` and returns a temperature in Kelvin\n",
+    "NCL's `dewtemp_trh` calculates the dew point temperature given temperature and relative humidity using the equations from John Dutton's _\"Ceaseless Wind\"_ (pg. 273-274){footcite}`dutton_1986` and returns a temperature in Kelvin.\n",
+    "\n",
+    "Where, for the gas constant of water vapor ({math}`R_{v}`)of 461.5 {math}`\\frac{J}{K*kg}` ({math}`\\frac{461.5}{1000 * 4.186} \\frac{cal}{g*k}`), the empirical value of the latent heat (pg. 273, Problem 8.3.1) is:\n",
+    "\n",
+    "{math}`L_{lv} = 597.3 - 0.57(T - 273)`\n",
+    "\n",
+    "So, when {math}`h` is the relative humidity, the dew point temperature (pg. 273, Equation 6, solved for as {math}`T_D`) is:\n",
+    "\n",
+    "{math}`T_D = \\frac{T * L_{lv}}{L_{lv} - R_{v}Tlog(h)}`\n",
     "\n",
     "<div class=\"admonition alert alert-info\">\n",
     "    <p class=\"admonition-title\" style=\"font-weight:bold\">Important Note</p>\n",
@@ -78,7 +86,15 @@
    "source": [
     "## daylight_fao56\n",
     "\n",
-    "NCL's `daylight_fao56` calculates the maximum number of daylight hours as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 [(Chapter 3, Equation 34)](https://www.fao.org/4/X0490E/x0490e07.htm#chapter%203%20%20%20meteorological%20data) {footcite}`allan_fao_1998`"
+    "NCL's `daylight_fao56` calculates the maximum number of daylight hours as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 [(Chapter 3, Equation 34)](https://www.fao.org/4/X0490E/x0490e07.htm#chapter%203%20%20%20meteorological%20data) {footcite}`allan_fao_1998`.\n",
+    "\n",
+    "Where the maximum number of daylight hours, {math}`N`, is:\n",
+    "\n",
+    "{math}`N = \\frac{24}{{\\pi}} {\\omega}_{s}`\n",
+    "\n",
+    "And {math}`{\\omega}_{s}` is the sunset hour angle in radians [(Chapter 3, Equation 25)](https://www.fao.org/4/X0490E/x0490e07.htm#chapter%203%20%20%20meteorological%20data) {footcite}`allan_fao_1998` which is calculated from the latitude of the observer on Earth ({math}`\\phi`) and the sun's declination ({math}`\\delta`):\n",
+    "\n",
+    "{math}`{\\omega}_{s} = arccos[-tan({\\phi})tan({\\delta})]`"
    ]
   },
   {
@@ -125,7 +141,11 @@
    "source": [
     "## satvpr_temp_fao56\n",
     "\n",
-    "NCL's `satvpr_temp_fao56` calculates saturation vapor pressure using temperature as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 [(Chapter 3, Equation 11)](https://www.fao.org/4/x0490e/x0490e07.htm) {footcite}`allan_fao_1998`"
+    "NCL's `satvpr_temp_fao56` calculates saturation vapor pressure using temperature as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 [(Chapter 3, Equation 11)](https://www.fao.org/4/x0490e/x0490e07.htm) {footcite}`allan_fao_1998`.\n",
+    "\n",
+    "Where the saturation vapor pressure, {math}`e^°` (kPa), at air temperature {math}`T` (°C) is calculated as:\n",
+    "\n",
+    "{math}`e^°(T) = 0.6108 {\\exp}[\\frac{17.27T}{T + 237.3}]`"
    ]
   },
   {
@@ -169,7 +189,11 @@
    "source": [
     "## satvpr_tdew_fao56\n",
     "\n",
-    "NCL's `satvpr_tdew_fao56` calculates the actual saturation vapor pressure using dewpoint temperature as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 [(Chapter 3, Equation 14)](https://www.fao.org/4/x0490e/x0490e07.htm) {footcite}`allan_fao_1998`"
+    "NCL's `satvpr_tdew_fao56` calculates the actual saturation vapor pressure using dewpoint temperature as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 [(Chapter 3, Equation 14)](https://www.fao.org/4/x0490e/x0490e07.htm) {footcite}`allan_fao_1998`.\n",
+    "\n",
+    "Where the actual vapor pressure, {math}`e_{a}` (kPa), is saturation vapor pressure at a specific dewpoint temperature, {math}`T_{dew}` (°C), which is calculated as:\n",
+    "\n",
+    "{math}`e_{a} = e^°(T_{dew}) = 0.6108 {\\exp}[\\frac{17.27 T_{dew}}{T_{dew} + 237.3}]`"
    ]
   },
   {
@@ -206,7 +230,11 @@
    "source": [
     "## satvpr_slope_fao56\n",
     "\n",
-    "NCL's `satvpr_slope_fao56` calculates the slope of the saturation vapor pressure curve as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 [(Chapter 3, Equation 13)](https://www.fao.org/4/x0490e/x0490e07.htm) {footcite}`allan_fao_1998`"
+    "NCL's `satvpr_slope_fao56` calculates the slope of the saturation vapor pressure curve as described in the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 [(Chapter 3, Equation 13)](https://www.fao.org/4/x0490e/x0490e07.htm) {footcite}`allan_fao_1998`.\n",
+    "\n",
+    "Where the slope of saturation vapor pressure curve, {math}`{\\Delta}` (kPa), at air temperature {math}`T` (°C) is calculated as:\n",
+    "\n",
+    "{math}`{\\Delta} = \\frac{4098 (0.6108 {\\exp}[\\frac{17.27T}{T + 237.3}])}{(T + 237.3)^2}`"
    ]
   },
   {