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fsa_N11.m
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% fas_N11: Function to calculate air-sea gas exchange flux using Nicholson
% 2011 parameterization
%
% USAGE:-------------------------------------------------------------------
%
% [Fd, Fc, Fp, Deq, k] = fsa_N11(C_w,C_a,u10,S,T,gas)
% T = 10; u10 = 12; S = 35;
% pAr = gasmolfract('Ar')*(1-vpress(35,10));
% [Fd, Fc, Fp, Deq, k] = fsa_N11(0.014,pAr,u10,S,T,'Ar')
%
% > Fd = 1.7501e-08
% > Fc = -1.4385e-08
% > Fp = -4.1141e-09
% > Deq = 0.0134
% > k = 1.0003e-04
%
% DESCRIPTION:-------------------------------------------------------------
%
% Calculate air-sea fluxes and steady-state supersaturation based on:
% Nicholson, D., S. Emerson, S. Khatiwala, R. C. Hamme. (in press)
% An inverse approach to estimate bubble-mediated air-sea gas flux from
% inert gas measurements. Proceedings on the 6th International Symposium
% on Gas Transfer at Water Surfaces. Kyoto University Press.
%
% Fc = Ainj * slpc * Xg * u3
% Fp = Aex * slpc * Geq * D^n * u3
%
% where u3 = (u-2.27)^3 (and zero for u < 2.27)
%
% Explanation of slpc:
% slpc = (observed dry air pressure)/(reference dry air pressure)
% slpc is a pressure correction factor to convert from reference to
% observed conditions. Equilibrium gas concentration in gasmoleq is
% referenced to 1 atm total air pressure, including saturated water vapor
% (RH=1), but observed sea level pressure is usually different from 1 atm,
% and humidity in the marine boundary layer can be less than saturation.
% Thus, the observed sea level pressure of each gas will usually be
% different from the reference.
%
% INPUTS:------------------------------------------------------------------
%
% Cw: dissolved gas concentration in mol m-3
% Ca: partial pressure in overlying atmospher (uatm)
% Ceq = K0 * Ca or also Ceq = K0 * xG * (slp - rh * vpress)
% where Ca is actual partial pressure (atm) and xG is dry mol/mol
% u10: 10 m wind speed (m/s)
% S: Sea surface salinity (PSS)
% T: Sea surface temperature (deg C)
% slp: sea level pressure (atm)
% rh: relative humidity (0 to 1)
%
% gas: formula for gas, formatted as a string, e.g. 'He'
% Code Gas name Reference
% ---- ---------- -----------
% He Helium Weiss 1971
% Ne Neon Hamme and Emerson 2004
% Ar Argon Hamme and Emerson 2004
% Kr Krypton Weiss and Keiser 1978
% Xe Xenon Wood and Caputi 1966
% N2 Nitrogen Hamme and Emerson 2004
% O2 Oxygen Garcia and Gordon 1992
%
% varargin: optional but recommended arguments
% rhum: relative humidity as a fraction of saturation (0.5 = 50% RH).
% If not provided, it will be automatically set to 1 (100% RH).
%
% OUTPUTS:-----------------------------------------------------------------
% Fd: Surface air-sea diffusive flux based on
% Sweeney et al. 2007 [mol m-2 s-1]
% Fc: Injection bubble flux (complete trapping) [mol m-2 s-1]
% Fp: Exchange bubble flux (partial trapping) [mol m-2 s-1]
% Deq: Steady-state supersaturation [unitless (%sat/100)]
% k: Diffusive gas transfer velocity (m s-1)
%
% Note: Total air-sea flux is Ft = Fd + Fc + Fp
%
% REFERENCE:---------------------------------------------------------------
% Nicholson, D., S. Emerson, S. Khatiwala, R. C. Hamme (2011)
% An inverse approach to estimate bubble-mediated air-sea gas flux from
% inert gas measurements. Proceedings on the 6th International Symposium
% on Gas Transfer at Water Surfaces. Kyoto University Press.
%
% AUTHORS:-----------------------------------------------------------------
% David Nicholson [email protected]
% Cara Manning [email protected]
% Woods Hole Oceanographic Institution
% Version 30 November 2017
%
% COPYRIGHT:---------------------------------------------------------------
%
% Copyright 2017 David Nicholson and Cara Manning
%
% Licensed under the Apache License, Version 2.0 (the "License");
% you may not use this file except in compliance with the License, which
% is available at http://www.apache.org/licenses/LICENSE-2.0
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Fd, Fc, Fp, Deq, k] = fsa_N11(Cw,Ca,u10,S,T,gas)
% 1.5 factor converts from average winds to instantaneous - see N11 ref.
Ainj = 2.51e-9./1.5;
Aex = 1.15e-5./1.5;
% Convert uatm to mmolm3
Ceq_molm3 = gasmolsol(S,T,Ca,gas);
xG = Ca ./ (1 - vpress(S,T));
[D,Sc] = gasmoldiff(S,T,gas);
% calculate wind speed term for bubble flux
u3 = (u10-2.27).^3;
u3(u3 < 0) = 0;
k = kgas(u10,Sc,'Sw07');
Fd = k.*(Cw-Ceq_molm3);
Fc = -Ainj.*xG.*u3;
Fp = -Aex.*Ceq_molm3.*D.^0.5.*u3;
Deq = -(Fc+Fp)./(k * Ceq_molm3);