ERF_SatMethods.H

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// This class contains all methods for estimating
// the saturation vapor pressure of water.
//
// wv_saturation provides specific interfaces and utilities
// based on these formulae.
//
// Typical usage of this module:
//
// Init:
// call wv_sat_methods_init(r8, <constants>, errstring)
//
// Get scheme index from a name string:
// scheme_idx = wv_sat_get_scheme_idx(scheme_name)
// if (.not. wv_sat_valid_idx(scheme_idx)) <throw some error>
//
// Get pressures:
// es = wv_sat_svp_water(t, scheme_idx)
// es = wv_sat_svp_ice(t, scheme_idx)
//
// Use ice/water transition range:
// es = wv_sat_svp_trice(t, ttrice, scheme_idx)
//
// Note that elemental functions cannot be pointed to, nor passed
// as arguments. If you need to do either, it is recommended to
// wrap the function so that it can be given an explicit (non-
// elemental) interface.
#ifndef ERF_SAT_METHOD_H_
#define ERF_SAT_METHOD_H_
 
#include <string>
#include <vector>
#include <memory>
#include <cmath>
 
#include "ERF_Constants.H"            // epsilo, omeps
#include "ERF_MicrophysicsConstants.H" // tmelt, h2otrip, tboil, ttrice
 
/**
 * @brief Methods for estimating the saturation vapor pressure of water.
 */
class SatMethods {
public:
    // Get saturation specific humidity given pressure and SVP.
    // Specific humidity is limited to range 0-1
    /**
     * @brief Get saturation specific humidity given pressure and SVP.
     * @param[in] es Saturation vapor pressure.
     * @param[in] p Total pressure.
     * @return Saturation specific humidity.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real wv_sat_svp_to_qsat (const amrex::Real& es, const amrex::Real& p) {
        // If pressure is less than SVP, set qs to maximum of amrex::Real(1)
        if ( (p - es) <= amrex::Real(0) )
            return amrex::Real(1);
        else
            return epsilo*es / (p - omeps*es);
    }
 
    /**
     * @brief Calculate SVP over water and saturation specific humidity.
     * @param[in] t Temperature.
     * @param[in] p Total pressure.
     * @param[out] es Saturation vapor pressure.
     * @param[out] qs Saturation specific humidity.
     * @param[in] idx Scheme index.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void wv_sat_qsat_water (const amrex::Real& t, const amrex::Real& p,
                                   amrex::Real &es, amrex::Real &qs, const int idx = 1) {
        // Purpose:
        //   Calculate SVP over water at a given temperature, and then
        //   calculate and return saturation specific humidity.
 
        es = wv_sat_svp_water(t, idx);
 
        qs = wv_sat_svp_to_qsat(es, p);
 
        // Ensures returned es is consistent with limiters on qs.
        es = std::min(es, p);
    }
 
    /**
     * @brief Calculate SVP over ice and saturation specific humidity.
     * @param[in] t Temperature.
     * @param[in] p Total pressure.
     * @param[out] es Saturation vapor pressure.
     * @param[out] qs Saturation specific humidity.
     * @param[in] idx Scheme index.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void wv_sat_qsat_ice (const amrex::Real& t, const amrex::Real& p,
                                 amrex::Real &es, amrex::Real &qs, const int idx = 1) {
        // Purpose:
        //   Calculate SVP over ice at a given temperature, and then
        //   calculate and return saturation specific humidity.
 
        es = wv_sat_svp_ice(t, idx);
 
        qs = wv_sat_svp_to_qsat(es, p);
 
        // Ensures returned es is consistent with limiters on qs.
        es = std::min(es, p);
    }
 
    /**
     * @brief Calculate transition SVP and saturation specific humidity.
     * @param[in] t Temperature.
     * @param[in] p Total pressure.
     * @param[out] es Saturation vapor pressure.
     * @param[out] qs Saturation specific humidity.
     * @param[in] idx Scheme index.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void wv_sat_qsat_trans (const amrex::Real& t, const amrex::Real& p,
                                   amrex::Real &es, amrex::Real &qs, const int idx = 1) {
        // Purpose:
        //   Calculate SVP over ice at a given temperature, and then
        //   calculate and return saturation specific humidity.
 
        es = wv_sat_svp_trans(t, idx);
 
        qs = wv_sat_svp_to_qsat(es, p);
 
        // Ensures returned es is consistent with limiters on qs.
        es = std::min(es, p);
    }
 
    // SVP INTERFACE FUNCTIONS
    /**
     * @brief Dispatcher for saturation vapor pressure over water.
     * @param[in] t Temperature.
     * @param[in] idx Scheme index.
     * @return Saturation vapor pressure over water.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real wv_sat_svp_water (const amrex::Real& t, const int idx = 1) {
        amrex::Real es;
        switch(idx)
            {
            case GoffGratch:
                es = GoffGratch_svp_water(t); break;
            case MurphyKoop:
                es = MurphyKoop_svp_water(t); break;
            case OldGoffGratch:
                es = OldGoffGratch_svp_water(t); break;
            case Bolton:
                es = Bolton_svp_water(t); break;
            }
        return es;
    }
 
    /**
     * @brief Dispatcher for saturation vapor pressure over ice.
     * @param[in] t Temperature.
     * @param[in] idx Scheme index.
     * @return Saturation vapor pressure over ice.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real wv_sat_svp_ice (const amrex::Real& t, const int idx = 1) {
        amrex::Real es;
        switch(idx)
            {
            case GoffGratch:
                es = GoffGratch_svp_ice(t); break;
            case MurphyKoop:
                es = MurphyKoop_svp_ice(t); break;
            case OldGoffGratch:
                es = OldGoffGratch_svp_ice(t); break;
            case Bolton:
                es = Bolton_svp_water(t); break;
            }
        return es;
    }
 
    /**
     * @brief Calculate transition saturation vapor pressure.
     * @param[in] t Temperature.
     * @param[in] idx Scheme index.
     * @return Transition saturation vapor pressure.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real wv_sat_svp_trans (const amrex::Real& t, const int idx = 1) {
        amrex::Real esice;      // Saturation vapor pressure over ice
        amrex::Real weight;     // Intermediate scratch variable for es transition
        amrex::Real es;
 
        // Water
        if (t >= (tmelt - ttrice))
            es = wv_sat_svp_water(t,idx);
        else
            es = amrex::Real(0);
 
        // Ice
        if (t < tmelt) {
            esice = wv_sat_svp_ice(t,idx);
            if ( (tmelt - t) > ttrice )
                weight = amrex::Real(1);
            else
                weight = (tmelt - t)/ttrice;
 
            es = weight*esice + (amrex::Real(1) - weight)*es;
        }
        return es;
    }
 
 
    // Goff & Gratch (1946)
    /**
     * @brief Goff & Gratch (1946) saturation vapor pressure over water.
     * @param[in] t Temperature.
     * @return Saturation vapor pressure.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real GoffGratch_svp_water (const amrex::Real& t) {
        // uncertain below -70 C
        return pow(amrex::Real(10.), (-amrex::Real(7.90298)*(tboil/t-amrex::Real(1))+
                         amrex::Real(5.02808)*std::log10(tboil/t)-
                         amrex::Real(1.3816e-7)*(pow(amrex::Real(10.), (amrex::Real(11.344)*(amrex::Real(1)-t/tboil)))-amrex::Real(1))+
                         amrex::Real(8.1328e-3)*(pow(amrex::Real(10.), (-amrex::Real(3.49149)*(tboil/t-amrex::Real(1))))-amrex::Real(1))+
                         std::log10(amrex::Real(1013.246))))*amrex::Real(100.);
    }
 
    /**
     * @brief Goff & Gratch (1946) saturation vapor pressure over ice.
     * @param[in] t Temperature.
     * @return Saturation vapor pressure.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real GoffGratch_svp_ice (const amrex::Real& t) {
        // good down to -100 C
        return pow(amrex::Real(10.), (-amrex::Real(9.09718)*(h2otrip/t-amrex::Real(1))-amrex::Real(3.56654)*
                         log10(h2otrip/t)+amrex::Real(0.876793)*(amrex::Real(1)-t/h2otrip)+
                         log10(amrex::Real(6.1071))))*amrex::Real(100.);
    }
 
    // Murphy & Koop (2005)
    /**
     * @brief Murphy & Koop (2005) saturation vapor pressure over water.
     * @param[in] t Temperature.
     * @return Saturation vapor pressure.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real MurphyKoop_svp_water (const amrex::Real& t) {
        // (good for 123 < T < 332 K)
        return exp(amrex::Real(54.842763) - (amrex::Real(6763.22) / t) - (amrex::Real(4.210) * log(t)) +
                   (amrex::Real(0.000367) * t) + (tanh(amrex::Real(0.0415) * (t - amrex::Real(218.8))) *
                                     (amrex::Real(53.878) - (amrex::Real(1331.22) / t) - (amrex::Real(9.44523) * log(t)) +
                                      amrex::Real(0.014025) * t)));
    }
 
    /**
     * @brief Murphy & Koop (2005) saturation vapor pressure over ice.
     * @param[in] t Temperature.
     * @return Saturation vapor pressure.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real MurphyKoop_svp_ice (const amrex::Real& t) {
        // (good down to 110 K)
        return exp(amrex::Real(9.550426) - (amrex::Real(5723.265) / t) + (amrex::Real(3.53068) * log(t))
                   - (amrex::Real(0.00728332) * t));
    }
 
 
    // Old CAM implementation, also labeled Goff & Gratch (1946)
 
    // The water formula differs only due to compiler-dependent order of
    // operations, so differences are roundoff level, usually zero
 
    // The ice formula gives fairly close answers to the current
    // implementation, but has been rearranged, and uses the
    // 1 atm melting point of water as the triple point.
    // Differences are thus small but above roundoff.
 
    // A curious fact: although using the melting point of water was
    // probably a mistake, it mildly improves accuracy for ice svp,
    // since it compensates for a systematic error in Goff & Gratch.
    /**
     * @brief Old CAM implementation of Goff & Gratch (1946) SVP over water.
     * @param[in] t Temperature.
     * @return Saturation vapor pressure.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real OldGoffGratch_svp_water (const amrex::Real& t) {
        auto ps = amrex::Real(1013.246);
        auto e1 = amrex::Real(11.344)*(amrex::Real(1) - t/tboil);
        auto e2 = -amrex::Real(3.49149)*(tboil/t - amrex::Real(1));
        auto f1 = -amrex::Real(7.90298)*(tboil/t - amrex::Real(1));
        auto f2 = amrex::Real(5.02808)*log10(tboil/t);
        auto f3 = -amrex::Real(1.3816)*(pow(amrex::Real(10.0), e1) - amrex::Real(1))/amrex::Real(10000000.0);
        auto f4 = amrex::Real(8.1328)*(pow(amrex::Real(10.0), e2) - amrex::Real(1))/amrex::Real(1000.0);
        auto f5 = log10(ps);
        auto f  = f1 + f2 + f3 + f4 + f5;
        return (pow(amrex::Real(10.0), f))*amrex::Real(100.0);
    }
 
    /**
     * @brief Old CAM implementation of Goff & Gratch (1946) SVP over ice.
     * @param[in] t Temperature.
     * @return Saturation vapor pressure.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real OldGoffGratch_svp_ice (const amrex::Real& t) {
        auto term1 = amrex::Real(2.01889049)/(tmelt/t);
        auto term2 = amrex::Real(3.56654)*log(tmelt/t);
        auto term3 = amrex::Real(20.947031)*(tmelt/t);
        return amrex::Real(575.185606e10)*exp(-(term1 + term2 + term3));
    }
 
    // Bolton (1980)
    // zm_conv deep convection scheme contained this SVP calculation.
    // It appears to be from D. Bolton, 1980, Monthly Weather Review.
    // Unlike the other schemes, no distinct ice formula is associated
    // with it. (However, a Bolton ice formula exists in CLUBB.)
 
    // The original formula used degrees C, but this function
    // takes Kelvin and internally converts.
    /**
     * @brief Bolton (1980) saturation vapor pressure over water.
     * @param[in] t Temperature.
     * @return Saturation vapor pressure.
     */
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real Bolton_svp_water (const amrex::Real& t) {
        constexpr auto c1 = amrex::Real(611.2);
        constexpr auto c2 = amrex::Real(17.67);
        constexpr auto c3 = amrex::Real(243.5);
        return c1*exp( (c2*(t - tmelt))/((t - tmelt)+c3) );
    }
 
    // private data
private:
    // Indices representing individual schemes
    enum Type {
               Invalid = -1,
               OldGoffGratch = 0,
               GoffGratch = 1,
               MurphyKoop = 2,
               Bolton = 3
    };
};
#endif