ERF_WaterVaporSaturation.H

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//
// This module provides an interface to water vapor saturation methods, providing
// saturation vapor pressure and related calculations to CAM.
//
// The original wv_saturation codes were introduced by J. J. Hack,
// February 1990. The code has been extensively rewritten since then,
// including a total refactoring in Summer 2012.
//
// Methods:
//
// Pure water/ice saturation vapor pressures are calculated on the
// fly, with the specific method determined by a runtime option.
//
// The default method for calculating SVP is determined by a namelist
// option, and used whenever svp_water/ice or qsat are called.
//
#ifndef ERF_WATER_VAPOR_SATURATION_H_
#define ERF_WATER_VAPOR_SATURATION_H_
 
#include <string>
#include <vector>
#include <memory>
 
#include "ERF_Constants.H"
#include "ERF_Sat_methods.H"
 
// Radiation code interface class
class WaterVaporSat {
public:
    // Make these public parameters in case another module wants to see the
    // extent of the table.
    static constexpr amrex::Real tmin = 127.16;
    static constexpr amrex::Real tmax = 375.16;
 
    // Set coefficients for polynomial approximation of difference
    // between saturation vapor press over water and saturation pressure
    // over ice for -ttrice < t < 0 (degrees C). NOTE: polynomial is
    // valid in the range -40 < t < 0 (degrees C).
    static constexpr int npcf = 5;
    static constexpr const amrex::Real pcf[npcf] = {5.04469588506e-01,
                                                   -5.47288442819e+00,
                                                   -3.67471858735e-01,
                                                   -8.95963532403e-03,
                                                   -7.78053686625e-05};
 
    // Compute saturation vapor pressure over water
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real svp_water (const amrex::Real& t) {
        return SatMethods::wv_sat_svp_water(t);
    }
 
    // Compute saturation vapor pressure over ice
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real svp_ice (const amrex::Real& t) {
        return SatMethods::wv_sat_svp_ice(t);
    }
 
    // Compute saturation vapor pressure with an ice-water transition
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real svp_trans (const amrex::Real& t) {
        return SatMethods::wv_sat_svp_trans(t);
    }
 
    // Get enthalpy based only on temperature
    // and specific humidity.
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static amrex::Real tq_enthalpy (const amrex::Real& t,
                                    const amrex::Real& q,
                                    const amrex::Real& hltalt) {
        return Cp_d * t + hltalt * q;
    }
 
    //------------------------------------------------
    // LATENT HEAT OF VAPORIZATION CORRECTIONS
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void no_ip_hltalt (const amrex::Real& t,
                              amrex::Real& hltalt) {
        hltalt = lat_vap;
        // Account for change of lat_vap with t above freezing where
        // constant slope is given by -2369 j/(kg c) = cpv - cw
        if (t >= tmelt) hltalt = hltalt - 2369.0*(t-tmelt);
    }
 
    //  Calculate latent heat of vaporization of water at a given
    //  temperature, taking into account the ice phase if temperature
    //  is below freezing.
    //  Optional argument also calculates a term used to calculate
    //  d(es)/dT within the water-ice transition range.
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void calc_hltalt (const amrex::Real& t,
                             amrex::Real& hltalt,
                             amrex::Real* tterm = nullptr) {
        amrex::Real tc, weight;
        no_ip_hltalt(t, hltalt);
        if (t < tmelt) {
            // Weighting of hlat accounts for transition from water to ice.
            tc = t - tmelt;
            if (tc >= -ttrice) {
                weight = -tc/ttrice;
 
                // polynomial expression approximates difference between es
                // over water and es over ice from 0 to -ttrice (C) (max of
                // ttrice is 40): required for accurate estimate of es
                // derivative in transition range from ice to water
 
                if (tterm)
                {
                    for(auto i = npcf-1; i > 0;  --i) *tterm = pcf[i] + tc*(*tterm);
                    *tterm = *tterm/ttrice;
                }
            }
            else {
                weight = 1.0;
            }
 
            hltalt = hltalt + weight*lat_ice;
        }
    }
 
    // Temperature derivative outputs, for qsat_*
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void deriv_outputs (const amrex::Real& t,
                               const amrex::Real& p,
                               const amrex::Real& es,
                               const amrex::Real& qs,
                               const amrex::Real& hltalt,
                               const amrex::Real& tterm,
                               amrex::Real& gam,
                               amrex::Real& dqsdt) {
 
        // Local variables
        amrex::Real desdt;        // d(es)/dt
        amrex::Real dqsdt_loc;    // local copy of dqsdt
 
        if (qs == 1.0) {
            dqsdt_loc = 0.;
        }
        else {
            desdt = hltalt*es/(R_v*t*t) + tterm;
            dqsdt_loc = qs*p*desdt/(es*(p-omeps*es));
        }
 
        dqsdt = dqsdt_loc;
        gam   = dqsdt_loc * (hltalt/Cp_d);
    }
 
    // Look up and return saturation vapor pressure from precomputed
    // table, then calculate and return saturation specific humidity.
    // Optionally return various temperature derivatives or enthalpy
    // at saturation.
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void qsat (const amrex::Real& t,
                      const amrex::Real& p,
                      amrex::Real& es,
                      amrex::Real& qs,
                      amrex::Real* gam = nullptr,
                      amrex::Real* dqsdt = nullptr,
                      amrex::Real* enthalpy = nullptr) {
        // Local variables
        amrex::Real hltalt;       // Modified latent heat for T derivatives
        amrex::Real tterm = 0.0;        // Account for d(es)/dT in transition region
 
        es = svp_trans(t); //estblf(t);
 
        qs = SatMethods::wv_sat_svp_to_qsat(es, p);
 
        // Ensures returned es is consistent with limiters on qs.
        es = std::min(es, p);
 
        // Calculate optional arguments.
        // "generalized" analytic expression for t derivative of es
        // accurate to within 1 percent for 173.16 < t < 373.16
        calc_hltalt(t, hltalt, &tterm);
 
        if (enthalpy)
        {
            *enthalpy = tq_enthalpy(t, qs, hltalt);
        }
 
        if (gam && dqsdt)
        {
            deriv_outputs(t, p, es, qs, hltalt, tterm, *gam, *dqsdt);
        }
    }
 
    // Calculate SVP over water at a given temperature, and then
    // calculate and return saturation specific humidity.
    // Optionally return various temperature derivatives or enthalpy
    // at saturation.
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void qsat_water (const amrex::Real& t,
                            const amrex::Real& p,
                            amrex::Real& es,
                            amrex::Real& qs,
                            amrex::Real* gam = nullptr,
                            amrex::Real* dqsdt = nullptr,
                            amrex::Real* enthalpy = nullptr) {
        // Local variables
        amrex::Real hltalt;       // Modified latent heat for T derivatives
 
        SatMethods::wv_sat_qsat_water(t, p, es, qs);
 
        // "generalized" analytic expression for t derivative of es
        // accurate to within 1 percent for 173.16 < t < 373.16
 
        no_ip_hltalt(t, hltalt);
 
        if (enthalpy)
        {
            *enthalpy = tq_enthalpy(t, qs, hltalt);
        }
 
        if (gam && dqsdt)
        {
            // For pure water/ice transition term is 0.
            deriv_outputs(t, p, es, qs, hltalt, 0., *gam, *dqsdt);
        }
    }
 
    //  Calculate SVP over ice at a given temperature, and then
    //  calculate and return saturation specific humidity.
    //  Optionally return various temperature derivatives or enthalpy
    //  at saturation.
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void qsat_ice (const amrex::Real& t,
                          const amrex::Real& p,
                          amrex::Real& es,
                          amrex::Real& qs,
                          amrex::Real& gam,
                          amrex::Real& dqsdt,
                          amrex::Real& enthalpy) {
        // Local variables
        amrex::Real hltalt;       // Modified latent heat for T derivatives
 
        SatMethods::wv_sat_qsat_ice(t, p, es, qs);
 
        // For pure ice, just add latent heats.
        hltalt = lat_vap + lat_ice;
 
        enthalpy = tq_enthalpy(t, qs, hltalt);
 
        // For pure water/ice transition term is 0.
        deriv_outputs(t, p, es, qs, hltalt, 0., gam, dqsdt);
    }
 
    //   find the wet bulb temperature for a given t and q
    //   in a longitude height section
    //   wet bulb temp is the temperature and spec humidity that is
    //   just saturated and has the same enthalpy
    //   if q > qs(t) then tsp > t and qsp = qs(tsp) < q
    //   if q < qs(t) then tsp < t and qsp = qs(tsp) > q
    //
    // Method:
    // a Newton method is used
    // first guess uses an algorithm provided by John Petch from the UKMO
    // we exclude points where the physical situation is unrealistic
    // e.g. where the temperature is outside the range of validity for the
    //      saturation vapor pressure, or where the water vapor pressure
    //      exceeds the ambient pressure, or the saturation specific humidity is
    //      unrealistic
    AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
    static void findsp (const amrex::Real& q,
                        const amrex::Real& t,
                        const amrex::Real& p,
                        const bool& use_ice,
                        amrex::Real& tsp,
                        amrex::Real& qsp,
                        int& status) {
 
        //
        // local variables
        //
        int iter = 8;    // max number of times to iterate the calculation
 
        amrex::Real es;                   // sat. vapor pressure
        amrex::Real gam;                  // change in sat spec. hum. wrt temperature (times hltalt/cpair)
        amrex::Real dgdt;                 // work variable
        amrex::Real g;                    // work variable
        amrex::Real hltalt;               // lat. heat. of vap.
        amrex::Real qs;                   // spec. hum. of water vapor
 
        // work variables
        amrex::Real t1, q1, dt, dq;
        amrex::Real qvd;
        amrex::Real r1b, c1, c2, c3;
        constexpr amrex::Real dttol = 1.e-4; // the relative temp error tolerance required to quit the iteration
        constexpr amrex::Real dqtol = 1.e-4; // the relative moisture error tolerance required to quit the iteration
        amrex::Real enin, enout;
 
        c3 = 287.04*(7.5*log(10.))/Cp_d;
 
        // Saturation specific humidity at this temperature
        if (use_ice) {
            qsat(t, p, es, qs);
        }
        else {
            qsat_water(t, p, es, qs);
        }
 
        // make sure a meaningful calculation is possible
        if (p <= 5.*es || qs <= 0. || qs >= 0.5 || t < tmin || t > tmax) {
            status = 1;
            // Keep initial parameters when conditions aren't suitable
            tsp = t;
            qsp = q;
            enin = 1.;
            enout = 1.;
            return;
        }
 
        // Prepare to iterate
        status = 2;
 
        // Get initial enthalpy
        if (use_ice)
            calc_hltalt(t,hltalt);
        else
            no_ip_hltalt(t,hltalt);
 
        enin = tq_enthalpy(t, q, hltalt);
 
        // make a guess at the wet bulb temp using a UKMO algorithm (from J. Petch)
        c1 = hltalt*c3;
        c2 = std::pow(t + 36., 2);
        r1b = c2/(c2 + c1*qs);
        qvd = r1b * (q - qs);
        tsp = t + ((hltalt/Cp_d)*qvd);
 
        // Generate qsp, gam, and enout from tsp.
        if (use_ice)
            qsat(tsp, p, es, qsp, &gam, &enout);
        else
            qsat_water(tsp, p, es, qsp, &gam, &enout);
 
        // iterate on first guess
        for(auto l = 1; l < iter; ++l) {
 
            g = enin - enout;
            dgdt = -Cp_d * (1 + gam);
 
            // New tsp
            t1 = tsp - g/dgdt;
            dt = abs(t1 - tsp)/t1;
            tsp = t1;
 
            // bail out if past end of temperature range
            if ( tsp < tmin ) {
                tsp = tmin;
                // Get latent heat and set qsp to a value
                // that preserves enthalpy.
                if (use_ice)
                    calc_hltalt(tsp,hltalt);
                else
                    no_ip_hltalt(tsp,hltalt);
 
                qsp = (enin - Cp_d*tsp)/hltalt;
                enout = tq_enthalpy(tsp, qsp, hltalt);
                status = 4;
                break;
            }
 
            // Re-generate qsp, gam, and enout from new tsp.
            if (use_ice)
                qsat(tsp, p, es, q1, &gam, &enout);
            else
                qsat_water(tsp, p, es, q1, &gam, &enout);
 
            dq = abs(q1 - qsp)/std::max(q1,1.e-12);
            qsp = q1;
 
            // if converged at this point, exclude it from more iterations
            if (dt < dttol && dq < dqtol) {
                status = 0;
                break;
            }
        }
        // Test for enthalpy conservation
        if (abs((enin-enout)/(enin+enout)) > 1.e-4) status = 8;
        return;
    }
};
#endif // ERF_WATER_VAPOR_SATURATION_H_