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inc_LW_e_all.m
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% Calculates all sky atmospheric emissivity based on a specified method for
% clear sky and a specified method for cloudy skies
%
% RELEASE NOTES
% Written by Mark Raleigh ([email protected]), Oct 2013)
% Version 2.0 Overhauled by Mark Raleigh (Feb 2015) to have structure inputs
%
% SYNTAX
% [LWdwn,e_all,e_clr] = inc_LW_e_all(M_INPUTS, M_PARAMS, M_OPTIONS)
%
% INPUTS
% M_INPUTS = structure with the following variables (must have exact name)
% TIME = time matrix (per time_builder.m format), same number of rows as other inputs
% Ta = air temperature, K or C (will assume C if mean is less than 40 C)
% eo = vapor pressure (kPa) - optional if RH is provided and option Method_vpr>0
% RH = fractional relative humidity
% c = time series of cloud fraction (0-1 range) for Method_all from 1-8
% s = solar index (0-1 range) for Method_all from 9-10
% tau = transmissiivty (0-1 range) for method 16
%
% M_PARAMS = structure with the coefficients used for the method. If you
% want to use the defaults, set M_PARAMS.P1 = []; or simply exclude the
% variable in the structure. Variables include:
% STA_Elev = elevation (m)
% P1_clr = 1xn array of parameter values for PARAMETER 1 (method-specific) for clear sky method
% P2_clr = 1xn array of parameter values for PARAMETER 2 (method-specific) for clear sky method
% ...
% Pn_clr = 1xn array of parameter values for PARAMETER n (method-specific) for clear sky method
%
% P1_all = 1xn array of parameter values for PARAMETER 1 (method-specific) for all sky method (cloud correction method)
% P2_all = 1xn array of parameter values for PARAMETER 2 (method-specific) for all sky method (cloud correction method)
% ...
% Pn_all = 1xn array of parameter values for PARAMETER n (method-specific) for all sky method (cloud correction method)
%
% M_OPTIONS = structure with options for the
% Method_vpr = if vapor pressure (eo) is not supplied in M_INPUTS,
% need to specify how to calculate it based on Ta and RH. Methods:
% 0 = do not calculate (eo is supplied)
% 1 = calculate with Dozier and Marks approach
% 2 = calculate with Clausius-Clapeyron e_sat in mb (hPa) from Murray 1967
% Method_clr = enter code for clear-sky longwave method, where:
% 1 = Angstrom (1918)
% 2 = Brunt (1932)
% 3 = Brutsaert (1975)
% 4 = Garratt (1992)
% 5 = Idso and Jackson (1969) (Idso-1)
% 6 = Idso (1981) (Idso-2)
% 7 = Iziomon et al. (2003)
% 8 = Keding (1989)
% 9 = Niemela et al. (2001)
% 10 = Prata (1996)
% 11 = Satterlund (1979)
% 12 = Swinbank (1963)
% 13 = Dilley and O'Brien (1998)
%
% %%% additional methods from Juszak and Pellicciotti (2013)
% 14 = Maykut and Church (1973)
% 15 = Konzelmann et al. (1994)
% 16 = Dilley and O'Brien (A) (1998)
%
% %%% other methods
% 17 = Campbell and Norman (1998) as cited by Walter et al (2005)
% 18 = Long and Turner (2008) - based on Brutsaert (1975)
% 19 = Ohmura (1982) as cited by Howard and Stull 2013
% 20 = Efimova (1961) as cited by Key et al (1996)
%
% Method_all = enter code for all-sky longwave method, where:
% %%% Cloud cover based methods
% 1 = Brutsaert (1982)
% 2 = Iziomon et al. (2003)
% 3 = Jacobs (1978)
% 4 = Keding (1989)
% 5 = Maykut and Church (1973)
% 6 = Sugita and Brutsaert (1993)
% 7 = Unsworth and Monteith (1975)
% 8 = Kimball et al. (1982)
% %%% Clearness/solar index based methods
% 9 = Crawford and Duchon (1999)
% 10 = Lhomme et al. (2007)
%
% %%% additional methods from Juszak and Pellicciotti (2013)
% 11 = Bolz (1949)
% 12 = Konzelmann et al (1994)
%
% %%% other methods
% 13 = Sicart et al (2006) (eqn 9, daily average transmissivity)
% 14 = Pirazzini et al (2000) as cited by Gubler (eqn 21)
% 15 = Pirazzini et al (2000) as cited by Gubler (eqn 22)
% 16 = Gubler et al (2012) eqn 23
% 17 = Zillman (1972) as cited by Key et al (1996)
% 18 = Duarte et al (2006) eqn 22
% 19 = Kruk et al (2010) eqn 18
% 20 = TVA (1972) as cited by Bras (1990)
%
% OUTPUTS
% LWdwn = incoming longwave (W m^-2)
% e_all = all-sky emissivity of the atmosphere
% e_clr = clear sky emissivity (prior to all-sky correction)
%
% NOTES
% The list of LW methods is populated based on Flerchinger et al. (2009).
% Additional empirical LW models may be added to this list.
function [LWdwn,e_all,e_clr] = inc_LW_e_all(M_INPUTS, M_PARAMS, M_OPTIONS)
%% constants
stefan = 5.67 * (10^-8); % Stefan-Boltzmann constant (J/s/m^2/K^4)
T_C2K = 273.15; % conversion from C to K
% E_L2W = 41840/86400; % conversion from langleys/day to W/m2
%% Checks
if M_OPTIONS.Method_clr-floor(M_OPTIONS.Method_clr)~=0 || M_OPTIONS.Method_clr < 1 || M_OPTIONS.Method_clr>20
error('Invalid M_OPTIONS.Method_clr')
end
if M_OPTIONS.Method_all-floor(M_OPTIONS.Method_all)~=0 || M_OPTIONS.Method_all < 1 || M_OPTIONS.Method_all>20
error('Invalid M_OPTIONS.Method_all')
end
% Now check to see if Ta is in Celsius, and if so, convert to K
if nanmean(nanmean(M_INPUTS.Ta)) < 40
% then assume the input was in Celsius
M_INPUTS.Ta = M_INPUTS.Ta + T_C2K;
end
% Now check to make sure RH is in fractional
if isfield(M_INPUTS, 'RH')==1
if nanmean(nanmean(M_INPUTS.RH)) > 1
disp('Assuming RH was input in percent. Converting to fractional')
M_INPUTS.RH = M_INPUTS.RH/100;
end
end
%% Common variables
Ta = M_INPUTS.Ta;
RH = M_INPUTS.RH;
if M_OPTIONS.Method_vpr==0
if isfield(M_INPUTS, 'eo') ~=1
error('eo must be provided in inputs, or include RH and specify method for computing eo')
end
eo = M_INPUTS.eo;
elseif M_OPTIONS.Method_vpr==1
error('this has not been coded yet')
elseif M_OPTIONS.Method_vpr==2
% Clausius-Clapeyron e_sat in mb (hPa) from Murray 1967
sat_vap_pressure = 6.1078.*exp((17.2693882.*(Ta-T_C2K))./(Ta-35.86));
eo = M_INPUTS.RH .* sat_vap_pressure;
% Convert eo from hPa to kPa
eo = eo./10;
end
c = M_INPUTS.c;
s = M_INPUTS.s;
tau =M_INPUTS.tau;
%%%%%%% at this point, eo should be in kPa and Ta should be in K
%% Method-specific default parameters
if M_OPTIONS.Method_all==1
% 1 = Brutsaert (1982)
nparams = 1;
P(1) = 0.22;
elseif M_OPTIONS.Method_all==2
% 2 = Iziomon et al. (2003)
nparams = 5;
P(1) = 0.35; P(2) = 212; P(3) = 0.50; P(4) = 1489; P(5) = 2;
elseif M_OPTIONS.Method_all==3
% 3 = Jacobs (1978)
nparams = 1;
P(1) = 0.26;
elseif M_OPTIONS.Method_all==4
% 4 = Keding (1989)
nparams = 2;
P(1) = 0.153; P(2) = 2.183;
elseif M_OPTIONS.Method_all==5
% 5 = Maykut and Church (1973)
nparams = 2;
P(1) = 0.22; P(2) = 2.75;
elseif M_OPTIONS.Method_all==6
% 6 = Sugita and Brutsaert (1993)
nparams = 2;
P(1) = 0.0496; P(2) = 2.45;
elseif M_OPTIONS.Method_all==7
% 7 = Unsworth and Monteith (1975)
% Note that this is the same as Campbell and Norman (1998) as cited by Walter et al (2005)
nparams = 2;
P(1) = 0.84; P(2) = 0.84;
elseif M_OPTIONS.Method_all==8
% 8 = Kimball et al. (1982)
nparams = 9;
P(1) = 11; P(2) = -0.6732; P(3) = 0.6240 .* (10^-2); P(4) = 0.9140 .* (10^-5);
P(5) = 0.24; P(6) = 2.98 .* (10^-6); P(7) = 3000; P(8) = 1.4; P(9) = 0.4;
elseif M_OPTIONS.Method_all==9
% 9 = Crawford and Duchon (1999)
nparams = 0;
elseif M_OPTIONS.Method_all==10
% 10 = Lhomme et al. (2007)
nparams = 2;
P(1) = 1.37; P(2) = 0.34;
elseif M_OPTIONS.Method_all==11
% 11 = Bolz (1949)
nparams = 2;
P(1) = 0.22; P(2) = 2.5;
elseif M_OPTIONS.Method_all==12
% 12 = Konzelmann et al (1994)
nparams = 2;
P(1) = 4; P(2) = 0.952;
elseif M_OPTIONS.Method_all==13
% 13 = Sicart et al (2006) (eqn 9, daily average transmissivity)
nparams = 2;
P(1) = 0.44;
P(2) = 0.18;
elseif M_OPTIONS.Method_all==14
% 14 = Pirazzini et al (2000) as cited by Gubler (eqn 21)
nparams = 2;
P(1) = 0.40; % a
P(2) = 2.00; % p0
elseif M_OPTIONS.Method_all==15
% 15 = Pirazzini et al (2000) as cited by Gubler (eqn 22)
nparams = 3;
P(1) = 0.979; % e_oc
P(2) = 6; % p1
P(3) = 4; % p2
elseif M_OPTIONS.Method_all==16
% 16 = Gubler et al (2012) eqn 23
nparams = 3;
P(1) = (0.968+0.985+0.940+0.928+0.987+0.926+0.828)/7; % e_oc value (average across 7 sites)
P(2) = (3.77+2.05+4.08+3.28+2.05+5.02+0.76)/7; % p1
P(3) = (2.97+1.61+2.94+2.57+1.78+3.74+1.24)/7; % p2
elseif M_OPTIONS.Method_all==17
% 17 = Zillman (1972) as cited by Key et al (1996)
nparams = 2;
P(1) = 0.96; P(2) = 9.2*10^-6;
elseif M_OPTIONS.Method_all==18
% 18 = Duarte et al (2006) eqn 22 - same form as Konzelmann
nparams = 2;
P(1) = 0.671; P(2) = 0.990;
elseif M_OPTIONS.Method_all==19
% 19 = Kruk et al (2010) eqn 18 - same form as Bolz, Duarte et al eqn 21, etc
nparams = 2;
P(1) = 0.1007; P(2) = 0.9061;
elseif M_OPTIONS.Method_all==20
% 20 = TVA (1972) as cited by Bras (1990) - same form as Bolz
nparams = 2;
P(1) = 0.17; P(2) = 2;
end
%% check for existence of parameters and set default values if no params were specified
if nparams>0
params_spec = zeros(1,nparams); % initialize variable to get size of each param
for j=1:nparams
%%% check if this parameter is a field
EXcheck = isfield(M_PARAMS, ['P' num2str(j) '_all']);
%%% if not, assign the default value
if EXcheck==0
eval(['M_PARAMS.P' num2str(j) '_all = P(j);']);
Px = P(j);
else
eval(['Px = M_PARAMS.P' num2str(j) '_all;']);
end
if isarray(Px) ~=1 && numel(Px)~=1
error('M_PARAMS.Pn_all variables should be single values or arrays')
end
params_spec(1,j) = numel(Px);
end
%%% assemble parameter sets
if nanvar(params_spec)~=0
error('All parameter sets must have the same number of elements')
else
if params_spec(1,1)>1
%%% need to do repeat matrix
for j=1:nparams
eval(['Px = M_PARAMS.P' num2str(j) '_all;']);
if size(Px,2)==1 && size(Px,1)>1
Px = Px';
end
eval(['M_PARAMS.P' num2str(j) '_all = repmat(Px, size(To,1), 1);']);
end
end
end
end
%% Code
%%% First, calculate clear-sky emissivity for the selected method
e_clr = inc_LW_e_clr(M_INPUTS, M_PARAMS, M_OPTIONS);
%%% double check to make sure we have e_clr within realistic limits [0 1]
e_clr(e_clr<0) = 0;
e_clr(e_clr>1) = 1;
%%% Now, calculate all-sky emissivity
if M_OPTIONS.Method_all==1
% 1 = Brutsaert (1982)
e_all = (1+ M_PARAMS.P1_all .*c).*e_clr;
elseif M_OPTIONS.Method_all==2
% 2 = Iziomon et al. (2003)
Mzz = (M_PARAMS.P3_all-M_PARAMS.P1_all)/(M_PARAMS.P4_all-M_PARAMS.P2_all);
Z = Mzz .*(M_PARAMS.STA_Elev - M_PARAMS.P2_all) + M_PARAMS.P1_all;
e_all = (1+Z.*c.^M_PARAMS.P5_all).*e_clr;
elseif M_OPTIONS.Method_all==3
% 3 = Jacobs (1978)
e_all = (1+ M_PARAMS.P1_all .*c).*e_clr;
elseif M_OPTIONS.Method_all==4
% 4 = Keding (1989)
e_all = (1+ M_PARAMS.P1_all .*c.^M_PARAMS.P2_all).*e_clr;
elseif M_OPTIONS.Method_all==5
% 5 = Maykut and Church (1973)
e_all = (1+ M_PARAMS.P1_all .*c.^M_PARAMS.P2_all).*e_clr;
elseif M_OPTIONS.Method_all==6
% 6 = Sugita and Brutsaert (1993)
e_all = (1+ M_PARAMS.P1_all .*c.^M_PARAMS.P2_all).*e_clr;
elseif M_OPTIONS.Method_all==7
% 7 = Unsworth and Monteith (1975)
e_all = (1-M_PARAMS.P1_all.*c).*e_clr + M_PARAMS.P2_all.*c;
elseif M_OPTIONS.Method_all==8
% 8 = Kimball et al. (1982)
Tc = Ta - M_PARAMS.P1_all; %%% no seasonal variation in Tc yet... could add in later
f8 = M_PARAMS.P2_all + M_PARAMS.P3_all.*Tc - M_PARAMS.P4_all.* Tc.^2;
e8z = M_PARAMS.P5_all + M_PARAMS.P6_all .* eo.^2 .* exp(M_PARAMS.P7_all./Ta);
tau8 = 1- e8z.*(M_PARAMS.P8_all-M_PARAMS.P9_all.*e8z);
Lclr = e_clr.*stefan.*Ta.^4;
Ld = Lclr + tau8.*c.*f8.*stefan.*(Tc.^4);
e_all = Ld./(stefan.*(Tc.^4)); % effective emissivity
%%% make sure e_all is in realistic limits [0 1]
e_all(e_all<0) = 0;
e_all(e_all>1) = 1;
%%% recalculate Ld
LWdwn = e_all.*stefan.*(Tc.^4); % note it is Tc not Ta for this method
elseif M_OPTIONS.Method_all==9
% 9 = Crawford and Duchon (1999)
e_all = (1-s) + s.*e_clr;
elseif M_OPTIONS.Method_all==10
% 10 = Lhomme et al. (2007)
e_all = (M_PARAMS.P1_all - M_PARAMS.P2_all.*s).*e_clr;
elseif M_OPTIONS.Method_all==11
% 11 = Bolz (1949)
e_all = e_clr.*(1+M_PARAMS.P1_all.*c.^M_PARAMS.P2_all);
elseif M_OPTIONS.Method_all==12
% 12 = Konzelmann et al (1994)
e_all = e_clr .*(1-c.^M_PARAMS.P1_all)+(M_PARAMS.P2_all.*c.^M_PARAMS.P1_all);
elseif M_OPTIONS.Method_all==13
% 13 = Sicart et al (2006) (eqn 9, daily average transmissivity)
if numel(tau)>1
tauD = TimeAverage(M_INPUTS.TIME,tau,'DAY');
else
tauD = tau;
end
e_all = e_clr.*(1+ M_PARAMS.P1_all.*RH - M_PARAMS.P2_all .* tauD);
elseif M_OPTIONS.Method_all==14
% 14 = Pirazzini et al (2000) as cited by Gubler (eqn 21)
e_all = e_clr.*(1+ M_PARAMS.P1_all.*c.^M_PARAMS.P2_all);
elseif M_OPTIONS.Method_all==15
% 15 = Pirazzini et al (2000) as cited by Gubler (eqn 22)
e_all = e_clr.*(1-c.^M_PARAMS.P2_all) + M_PARAMS.P1_all.*c.^M_PARAMS.P3_all;
elseif M_OPTIONS.Method_all==16
% 16 = Gubler et al (2012) eqn 23
if numel(tau)>1
tauD = TimeAverage(M_INPUTS.TIME,tau,'DAY');
else
tauD = tau;
end
e_all= (e_clr.*tauD.^M_PARAMS.P3_all) + M_PARAMS.P1_all.*(1-tauD.^M_PARAMS.P2_all);
elseif M_OPTIONS.Method_all==17
% 17 = Zillman (1972) as cited by Key et al (1996)
e_all = e_clr + M_PARAMS.P1_all.*(1-M_PARAMS.P2_all).*c;
elseif M_OPTIONS.Method_all==18
% 18 = Duarte et al (2006) eqn 22 - same form as Konzelmann
e_all = e_clr .*(1-s.^M_PARAMS.P1_all)+(M_PARAMS.P2_all.*s.^M_PARAMS.P1_all);
elseif M_OPTIONS.Method_all==19
% 19 = Kruk et al (2010) eqn 18 - same form as Bolz, Duarte et al eqn 21, etc
e_all = e_clr.*(1+M_PARAMS.P1_all.*s.^M_PARAMS.P2_all);
elseif M_OPTIONS.Method_all==20
% 20 = TVA (1972) as cited by Bras (1990) - same form as Bolz
e_all = e_clr.*(1+M_PARAMS.P1_all.*c.^M_PARAMS.P2_all);
end
if M_OPTIONS.Method_all ~= 8
%%% make sure e_all is in realistic limits [0 1]
e_all(e_all<0) = 0;
e_all(e_all>1) = 1;
LWdwn = e_all.*stefan.*Ta.^4;
end