MeteoLib.cs

using System;
using System.CodeDom;

namespace ImportWLK
{
	internal static class MeteoLib
	{

		/// <summary>
		/// Calculates the Wind Chill in Celsius
		/// </summary>
		/// <remarks>
		/// JAG/TI - 2003
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="windSpeedKph">Average wind speed in km/h</param>
		/// <param name="tempCutoff">Use the 10C cut-off</param>
		/// <returns>Wind Chill in Celsius</returns>
		public static double WindChill(double tempC, double windSpeedKph, bool tempCutoff = true)
		{
			// see American Meteorological Society Journal
			// see http://www.msc.ec.gc.ca/education/windchill/science_equations_e.cfm
			// see http://www.weather.gov/os/windchill/index.shtml

			if ((tempC >= 10.0 && tempCutoff) || (windSpeedKph <= 4.8))
				return tempC;

			double windPow = Math.Pow(windSpeedKph, 0.16);

			double wc = 13.12 + (0.6215 * tempC) - (11.37 * windPow) + (0.3965 * tempC * windPow);

			if (wc > tempC) return tempC;

			return wc;
		}

		/// <summary>
		/// Calculates Apparent Temperature in Celsius
		/// </summary>
		/// <remarks>
		/// See http://www.bom.gov.au/info/thermal_stress/#atapproximation
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="windspeedMS">Wind speed in m/s</param>
		/// <param name="humidity">Relative humidity</param>
		/// <returns>Apparent temperature in Celsius</returns>
		public static double ApparentTemperature(double tempC, double windspeedMS, int humidity)
		{
			double avp = (humidity / 100.0) * 6.105 * Math.Exp(17.27 * tempC / (237.7 + tempC)); // hPa
			//double avp = ActualVapourPressure(tempC, humidity)
			return tempC + (0.33 * avp) - (0.7 * windspeedMS) - 4.0;
		}

		/// <summary>
		/// Calculates the Feels Like temperature in Celsius
		/// </summary>
		/// <remarks>
		/// Joint Action Group for Temperature Indices (JAG/TI) formula
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="windSpeedKph">Wind speed in kph</param>
		/// <param name="humidity">Relative humidity</param>
		/// <returns>Feels Like temperature in Celsius</returns>
		public static double FeelsLike(double tempC, double windSpeedKph, int humidity)
		{
			double chill = WindChill(tempC, windSpeedKph, false);
			double svp = SaturationVapourPressure1980(tempC);   // Saturation Vapour Pressure in hPa
			double avp = (float) humidity / 100.0 * svp / 10.0;             // Actual Vapour Pressure in kPa
			if (windSpeedKph > 72) windSpeedKph = 72;           // Windspeed limited to 20 m/s = 72 km/h
			double apptemp = (1.04 * tempC) + (2 * avp) - (windSpeedKph * 0.1805553) - 2.7;
			double feels;
			if (tempC < 10.0)
			{
				feels = chill;
			}
			else if (tempC > 20.0)
			{
				feels = apptemp;
			}
			else
			{
				// 10-20 C = linear interpolation between chill and apparent
				double A = (tempC - 10) / 10;
				double B = 1 - A;
				feels = (apptemp * A) + (chill * B);
			}
			return feels;
		}



		/// <summary>
		/// Calculates the North American Heat Index
		/// </summary>
		/// <remarks>
		/// Uses the NOAA formula and corrections
		/// see: https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="humidity">Relative humidity</param>
		/// <returns>Heat Index in Celsius</returns>
		public static double HeatIndex(double tempC, int humidity)
		{
			double tempF = CToF(tempC);

			if (tempF < 80)
			{
				return tempC;
			}
			else
			{
				double tempSqrd = tempF * tempF;

				double humSqrd = humidity * humidity;

				var result = FtoC(0 - 42.379 + (2.04901523 * tempF) + (10.14333127 * humidity) - (0.22475541 * tempF * humidity) - (0.00683783 * tempSqrd) - (0.05481717 * humSqrd) +
					(0.00122874 * tempSqrd * humidity) + (0.00085282 * tempF * humSqrd) - (0.00000199 * tempSqrd * humSqrd));

				// Rothfusz adjustments
				if ((humidity < 13) && (tempF >= 80) && (tempF <= 112))
				{
					result -= ((13 - humidity) / 4.0) * Math.Sqrt((17 - Math.Abs(tempF - 95)) / 17.0);
				}
				else if ((humidity > 85) && (tempF >= 80) && (tempF <= 87))
				{
					result += ((humidity - 85) / 10.0) * ((87 - tempF) / 5.0);
				}

				return result;
			}
		}

		/// <summary>
		/// Estimates the Wet Bulb temperature using a polynomial
		/// </summary>
		/// <remarks>
		/// To calculate this accurately we need an iterative process
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="dewPointC">Dew point in C</param>
		/// <param name="pressureMb">Station pressure in mb/hPa</param>
		/// <returns>Wet bulb temperature in Celsius</returns>
		public static double CalculateWetBulbC(double tempC, double dewPointC, double pressureMb)
		{
			double svpDP = SaturationVapourPressure1980(dewPointC);

			return (((0.00066 * pressureMb) * tempC) + ((4098 * svpDP) / (Sqr(dewPointC + 237.7)) * dewPointC)) / ((0.00066 * pressureMb) + (4098 * svpDP) / (Sqr(dewPointC + 237.7)));
		}

		/// <summary>
		/// Estimates the Wet Bulb temperature using a polynomial
		/// </summary>
		/// <remarks>
		/// To calculate this accurately we need an iterative process
		/// This method assumes a pressure of 1013.25 hPa, and RH in the range 5% - 99%
		/// It is an empirical approximation generated using a best fit function
		/// See: https://journals.ametsoc.org/jamc/article/50/11/2267/13533/Wet-Bulb-Temperature-from-Relative-Humidity-and
		/// and Strull: https://www.eoas.ubc.ca/books/Practical_Meteorology/prmet102/Ch04-watervapor-v102b.pdf
		/// Errors have multiple relative maxima and minima of order from −1.0° to +0.6°C
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="humidity">Relative Humidity in %</param>
		/// <param name="PressureMB">Station pressure in mb/hPa</param>
		/// <returns>Wet bulb temperature in Celsius</returns>
		public static double CalculateWetBulbC2(double tempC, int humidity)
		{
			if (humidity == 100)
				return tempC;

			return tempC * Math.Atan(0.151977 * Math.Sqrt(humidity + 8.313659)) + Math.Atan(tempC + humidity) - Math.Atan(humidity - 1.676331) + 0.00391838 * Math.Pow(humidity, 3.0 / 2) * Math.Atan(0.023101 * humidity) - 4.686035;
		}


		/// <summary>
		/// Calculates the Wet Bulb temperature iteratively
		/// </summary>
		/// <remarks>
		/// To calculate this accurately we need an iterative process
		/// See: https://www.researchgate.net/publication/303156836_Simple_Iterative_Approach_to_Calculate_Wet-Bulb_Temperature_for_Estimating_Evaporative_Cooling_Efficiency
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="humidity">Relative Humidity in %</param>
		/// <param name="pressureHpa">Station pressure in mb/hPa</param>
		/// <returns>Wet bulb temperature in Celsius</returns>
		public static double CalculateWetBulbCIterative(double tempC, int humidity, double pressureHpa)
		{
			if (humidity == 100)
				return tempC;

			var e = ActualVapourPressure2008(tempC, humidity);
			double Tw;
			double Tw1 = tempC;

			do
			{
				Tw = Tw1;
				var Ewg = SaturationVapourPressure1980(Tw);
				var eg = Ewg - pressureHpa * (tempC - Tw) * 0.00066 * (1 + (0.00115 * Tw));
				var Ed = e - eg;
				Tw1 = Tw + Ed / 5 * 2;
			} while (Math.Abs(Tw - Tw1) > 0.1);

			return Tw1;
		}


		private static double Sqr(double num)
		{
			return num * num;
		}

		/// <summary>
		/// Calculates the Dew Point in Celsius
		/// </summary>
		/// <remarks>
		/// Uses the Davis formula, described as "an approximation of the Goff & Gratch equation"
		/// It is functionally equivalent to the Magnus formula using the Sonntag 1990 values for constants
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="humidity">Relative humidity</param>
		/// <returns>Dew Point temperature in Celsius</returns>
		public static double DewPoint(double tempC, double humidity)
		{
			if (humidity == 0 || humidity == 100)
				return tempC;

			// Davis algorithm
			double lnVapor = Math.Log(ActualVapourPressure2008(tempC, (int) humidity));
			return ((243.12 * lnVapor) - 440.1) / (19.43 - lnVapor);
		}

		/// <summary>
		/// Calculates the Saturated Vapour Pressure in hPa
		/// </summary>
		/// <remarks>
		/// Bolton(1980) or
		/// August–Roche–Magnus?
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <returns>SVP in hPa</returns>
		public static double SaturationVapourPressure1980(double tempC)
		{
			return 6.112 * Math.Exp(17.67 * tempC / (tempC + 243.5));
		}

		/// <summary>
		/// Calculates the Saturated Vapour Pressure in hPa
		/// </summary>
		/// <remarks>
		/// WMO - CIMO Guide - 2008
		/// Sonntag 1990
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <returns>SVP in hPa</returns>
		public static double SaturationVapourPressure2008(double tempC)
		{
			return 6.112 * Math.Exp((17.62 * tempC) / (243.12 + tempC));
		}

		private static double ActualVapourPressure2008(double tempC, int humidity)
		{
			return humidity / 100.0 * SaturationVapourPressure2008(tempC);
		}

		/// <summary>
		/// Calculates the Canadian Humidex
		/// </summary>
		/// <remarks>
		/// WMO - CIMO Guide - 2008
		/// Sonntag 1990
		/// </remarks>
		/// <param name="tempC">Temp in C</param>
		/// <param name="humidity">Relative humidity</param>
		/// <returns>Humidex - dimensionless</returns>
		public static double Humidex(double tempC, int humidity)
		{
			if (tempC < 10)
				return tempC;
			else
				return tempC + ((5.0 / 9.0) * (ActualVapourPressure2008(tempC, humidity) - 10.0));
		}

		public static double CToF(double tempC)
		{
			return ((tempC * 9.0) / 5.0) + 32;
		}

		public static double FtoC(double tempF)
		{
			return ((tempF - 32) * 5.0) / 9.0;
		}

		/// <summary>
		/// Calculates the Growing Degree Days.
		/// Uses method A - https://en.wikipedia.org/wiki/Growing_degree-day
		/// </summary>
		/// <param name="maxC">The days maximum temperature (Celsius)</param>
		/// <param name="minC">The days minimum temperature (Celsius)</param>
		/// <param name="baseC">The GDD base temperature (Celsius)</param>
		/// <returns>GrowingDegreeDay (Celsius)</returns>
		public static double GrowingDegreeDays(double maxC, double minC, double baseC, bool cap30C)
		{

			var hiC = cap30C && maxC > 30 ? 30 : maxC;
			var loC = cap30C && minC > 30 ? 30 : minC;
			var avgC = (hiC + loC) / 2;
			var gdd = 0.0;
			if (avgC > baseC)
			{
				gdd = avgC - baseC;
			}
			return gdd;
		}

		/// <summary>
		/// Calculates the Davis THW Index.
		/// Uses method described for Heat Index and THSW Index in AN28
		/// </summary>
		/// <param name="tempC">The current temperature (Celsius)</param>
		/// <param name="int">The current RH</param>
		/// <param name="windKph">The current average wind speed (KPH)</param>
		/// <returns>THWIndex (Celsius)</returns>

		public static double THWIndex(double tempC, int hum, double windKph)
		{
			var hindex = HeatIndex(tempC, hum);

			// above 144F/62.22C wind factor is zero
			var wind = tempC > 62.22 ? 0 : tempC - WindChill(tempC, windKph, false);

			return hindex - wind;
		}


		/// <summary>
		/// Calculates the sea leavel pressure
		/// </summary>
		/// <param name="altitudeM">Altitude in metres</param>
		/// <param name="pressureHpa">Station pressure in hPha</param>
		/// <param name="tempC">Current temperature</param>
		/// <returns>Returns the sea level pressure in hPa</returns>
		public static double GetSeaLevelPressure(double altitudeM, double pressureHpa, double tempC)
		{
			/* constants */
			double i = 287.05;// gas constant for dry air
			double a = 9.80665;// gravity
			double r = .0065; //standard atmosphere lapse rate
			double s = 1013.25;// standard sea level pressure
			double n = 273.15 + tempC; //288.15  standard sea level temp;

			double l = a / (i * r);
			double c = i * r / a;
			double u = Math.Pow(1 + Math.Pow(s / pressureHpa, c) * (r * altitudeM / n), l);
			double d = pressureHpa * u;
			return d;
		}

		/// <summary>
		/// Calculates the sea leavel pressure
		/// https://www.wind101.net/sea-level-pressure-advanced/LAPLACE%20GENERAL%20EQUATION%20THE%20REDUCTION%20OF%20BAROMETRIC%20PRESSURE%20DrKFS_net.pdf
		/// </summary>
		/// <param name="altitudeM">Station altitude in metres</param>
		/// <param name="pressureHpa">Station pressure in inHg</param>
		/// <param name="tempC">Current temperature</param>
		/// <param name="latitude">Latitude of the station</param>
		/// <returns>Returns the sea level pressure in hPa</returns>
		public static double GetSeaLevelPressure(double altitudeM, double pressureHpa, double tempC, decimal latitude)
		{
			/* constants */
			double latRad = (double) latitude * Math.PI / 180;   // Latitude in radians
			double R = 6367324;                         // Radius of Earth (m)
			double k = 0.0026;                          // asphericity of earth
			double K = 18400.0;                         // barometrics constant (m)
			double s = 1013.25;                         // standard sea level pressure (hPa)
			double r = .005;                            // atmosphere lapse rate assuming a temperature gradient of 0.5 degC/100 metres (C/m)
			double a = 0.0037;                          // coefficient of thermal expansion of the air

			double avgTemp = tempC + (r * altitudeM) / 2;                           // avg temp of air column
			double vp = Math.Pow(10, 7.5 * avgTemp / (237.3 + avgTemp)) * 6.1078;   // vapour pressure
			double corT = 1 + a * avgTemp;                                          // correction for atmospheric temperature
			double corH = 1 / (1 - 0.378 * (vp / s));                               // correction for humidity
			double corE = 1 / (1 - (k * Math.Cos(2 * latRad)));                     // correction for asphericity of earth
			double corG = 1 + altitudeM / R;                                        // correction for variation of gravity with height

			double corr = altitudeM / (K * corT * corH * corE * corG);

			return pressureHpa * Math.Pow(10, corr);
		}


		/// <summary>
		/// Calculates the sea leavel pressure using the Davis method
		/// http://www.fao.org/3/x0490e/x0490e07.htm#radiation - equation (39)
		/// </summary>
		/// <param name="altitudeFt">Altitude in feet</param>
		/// <param name="pressInHg">Station pressure in inHg</param>
		/// <param name="tempAvgT">Average of temperature now and temperature 12 hours ago</param>
		/// <param name="dewPoint">Current dewpoint</param>
		/// <returns>Returns the sea level pressure in inHG</returns>
		public static double GetSeaLevelPressureDavis(double altitudeFt, double pressInHg, double tempAvgT, double dewPoint)
		{
			throw new NotImplementedException();
		}


		/// <summary>
		/// Calculates the altimeter pressure
		/// </summary>
		/// <param name="pressureHpa">Station pressure in inHg</param>
		/// <param name="altitudeM">Station altitude in metres</param>
		/// <returns>Returns the altimeter pressure in hPa</returns>
		public static double StationToAltimeter(double pressureHPa, double elevationM)
		{
			// from MADIS API by NOAA Forecast Systems Lab, see http://madis.noaa.gov/madis_api.html

			double k1 = 0.190284; // discrepancy with calculated k1 probably because Smithsonian used less precise gas constant and gravity values
			double k2 = 8.4184960528E-5; // (standardLapseRate / standardTempK) * (Power(standardSLP, k1)
			return Math.Pow(Math.Pow(pressureHPa - 0.3, k1) + (k2 * elevationM), 1 / k1);
		}



		/// <summary>
		/// Calculates the net long wave radiation
		/// http://www.fao.org/3/x0490e/x0490e07.htm#radiation - equation (39)
		/// </summary>
		/// <param name="tempMinC">Minimum temperature over the period</param>
		/// <param name="tempMaxC">Maximum temperature over the period</param>
		/// <param name="vapPresskPa">Vapour pressure in kPa</param>
		/// <param name="radMeasured">Measured solar radiation (same units as radClearSky)</param>
		/// <param name="radClearSky">Calculated clear sky radiation (same units as radMeasured)</param>
		/// <returns>Returns the long wave (back) radiation in MJ/m^2/hour</returns>
		private static double LongwaveRadiation(double tempAvgC, double vapPresskPa, double radMeasured, double radClearSky)
		{
			var avgK = tempAvgC + 273.16;

			// Stefan-Boltzman constant in MJ/K^4/m^2/day
			var sigma = 4.903e-09;
			// because we are using 1 hour, it needs scaling...
			sigma /= 24.0;

			// Use the ratio of measured to expected radiation as a measure of cloudiness, but only if it's daylight
			double cloudFactor;
			if (radClearSky > 0)
			{
				cloudFactor = radMeasured / radClearSky;
				if (cloudFactor > 1)
					cloudFactor = 1;
			}
			else
			{
				// It's night!
				// As the night time ET is low compared to day, let's just assume 50% cloud cover
				cloudFactor = 0.5;
			}

			// Calculate the long wave (back) radiation in MJ/m^2/hour.
			var part1 = sigma * Math.Pow(avgK, 4);
			var part2 = (0.34 - 0.14 * Math.Sqrt(vapPresskPa));
			var part3 = (1.35 * cloudFactor - 0.35);

			return part1 * part2 * part3;
		}

		/// <summary>
		///  Evapotranspiration
		///  The calculation of ETo by means of the FAO Penman-Monteith equation
		///  Using grass as the reference crop
		///  Uses the "hourly time step" equations - http://www.fao.org/3/x0490e/x0490e08.htm#calculation%20procedure
		///  With acknowledgement to the equivalent WeeWX formula - https://github.com/weewx/weewx/blob/master/bin/weewx/wxformulas.py
		/// </summary>
		/// <param name="tempMinC"></param>
		/// <param name="tempMaxC"></param>
		/// <param name="humMin"></param>
		/// <param name="humMax"></param>
		/// <param name="radMean">Mean solar irradiation over the period in W/m^2</param>
		/// <param name="windAvgMs">Mean wind speed over the period in m/s</param>
		/// <param name="latitude"></param>
		/// <param name="longitude"></param>
		/// <param name="altitudeM">Station altitude in metres</param>
		/// <param name="pressMinKpa"></param>
		/// <param name="pressMaxkpa"></param>
		/// <param name="date">Date/time of the end of the period</param>
		/// <returns>Evapotranspiration in mm</returns>
		public static double Evapotranspiration(
			double tempAvgC, int humAvg,
			double radMean, double maxRadMean, double windAvgMs,
			double pressKpa)
		{
			var windHeightM = 2.0; // height of wind sensor in metres, we assume 2m for a typical amateur station

			// Use grass as the reference crop
			var albedo = 0.23;

			// Adjust avg wind speed to a height of 2m (equation 47)
			var u2 = 4.87 * windAvgMs / Math.Log(67.8 * windHeightM - 5.42);

			// Calculate the psychrometric constant in kPa/C (equation 8)
			var gamma = 0.665e-03 * pressKpa;

			// Calculate mean saturation vapour pressure, converting from hPa to kPa (equation 12)
			var e0T = 0.6108 * Math.Exp(17.27 * tempAvgC / (tempAvgC + 237.3));

			// Calculate the slope of the saturation vapour pressure curve in kPa/C (equation 13)
			var delta = 4098.0 * (0.6108 * Math.Exp(17.27 * tempAvgC / (tempAvgC + 237.3))) / ((tempAvgC + 237.3) * (tempAvgC + 237.3));

			// Calculate actual vapour pressure from relative humidity (equation 17)
			var ea = e0T * humAvg / 100;

			// Convert solar radiation from W/m^2 to MJ/m^2/h
			var Rs = radMean * 0.0036;

			// Net short-wave (measured) radiation in MJ/m^2/h (equation 38)
			var Rns = (1 - albedo) * Rs;

			// Take the mean solar max and convert from W/m^2 to MJ/m^2/h
			var Rso = maxRadMean * 0.0036;

			// Long-wave (back) radiation. (equation 39 modified to per hour)
			var Rnl = LongwaveRadiation(tempAvgC, ea, Rs, Rso);

			// Calculate net radiation at the surface in MJ/m^2/h (equation 40)
			var Rn = Rns - Rnl;

			// Calculate the soil heat flux. (see section "For hourly or shorter periods" in http://www.fao.org/docrep/x0490e/x0490e07.htm#radiation
			var Ghr = (Rs > 0 ? 0.1 : 0.5) * Rn;

			// Result is in mm/h (equation 53)
			// But as we have fixed a 1 hour period, then the effective result is just mm
			var et0 = (0.408 * delta * (Rn - Ghr) + gamma * 37 / (tempAvgC + 273) * u2 * (e0T - ea)) / (delta + gamma * (1 + 0.34 * u2));

			if (et0 < 0) et0 = 0;

			return et0;
		}

		/// <summary>
		/// Calculates the Davis version (almost) of Evapotranspiration
		/// </summary>
		/// <returns>ET for past hour in mm</returns>
		/*
		public static double CalulateEvapotranspiration(DateTime ts)
		{
			var onehourago = ts.AddHours(-1);

			// Mean temperature in Fahrenheit
			var result = RecentDataDb.Query<AvgData>("select avg(OutsideTemp) temp, avg(WindSpeed) wind, avg(SolarRad) solar, avg(Humidity) hum from RecentData where Timestamp >= ?", onehourago);

			var meanTempC = ConvertUnits.UserTempToC(result[0].temp);
			var meanTempK = meanTempC + 273.16;
			var meanWind = ConvertUnits.UserWindToMS(result[0].wind);
			var meanHum = result[0].hum;
			var meanSolar = result[0].solar;
			var pressure = ConvertUnits.UserPressToMB(AltimeterPressure) / 100;  // need kPa

			var satVapPress = SaturationVapourPressure2008(meanTempC);
			var waterVapour = satVapPress * meanHum / 100;

			var delta = satVapPress / meanTempK * ((6790.4985 / meanTempK) - 5.02808);

			var gamma = 0.000646 * (1 + 0.000946 * meanTempC) * pressure;

			var weighting = delta / (delta + gamma);

			double windFunc;
			if (meanSolar > 0)
				windFunc = 0.030 + 0.0576 * meanWind;
			else
				windFunc = 0.125 + 0.0439 * meanWind;

			var lambda = 69.5 * (1 - 0.000946 * meanTempC);

			//TODO: Need to calculate the net radiation rather than use meanSolar - need mean theoretical solar value for this
			var meanSolarMax = 0.0; //TODO

			// clear sky - meanSolar/meanSolarMax >= 1, c <= 1, solar elevation > 10 deg
			var clearSky = (1.333 - 1.333 * meanSolar / meanSolarMax);

			var netSolar = 0.0; //TODO

			var ET = weighting * netSolar / lambda + (1 - weighting) * (satVapPress - waterVapour) * windFunc;

			return ET;
		}
		*/
	}
}