MARRMOT_09
Implementation
MARRMoT v2.1.1 rev eeb7e15 m_09_susannah1_6p_2s; standardized continuous structure, not original model
Time step: daily
Backend: octave-cli + Octave optim
Calibrated parameters: 6
Temperature required: no
Parameters and initial configuration
Parameter |
Supported calibration range |
Default |
|---|---|---|
|
1 to 2000 |
1000.5 |
|
0.05 to 0.95 |
0.5 |
|
0.05 to 0.95 |
0.5 |
|
1 to 50 |
25.5 |
|
0.2 to 1 |
0.6 |
|
0 to 1 |
0.5 |
|
Fixed initial/configuration value |
0.0 |
|
Fixed initial/configuration value |
0.0 |
Ranges/defaults are implementation contracts, not universal priors or a recommended basin calibration. Consult source comments for parameter units and coupling.
Governing equations
The following source is the exact model kernel used by this adapter. For MARRMoT it includes the state derivative and each referenced flux function; the solver and routing are described above. Original notices and source citations are retained in the files.
function [dS, fluxes] = model_fun(obj, S)
% parameters
theta = obj.theta;
sb = theta(1); % Maximum soil moisture storage [mm]
sfc = theta(2); % Wiliting point as fraction of sb [-]
m = theta(3); % Fraction forest [-]
a = theta(4); % Runoff coefficient [d]
b = theta(5); % Runoff coefficient [-]
r = theta(6); % Runoff coefficient [d-1]
% delta_t
delta_t = obj.delta_t;
% stores
S1 = S(1);
S2 = S(2);
% climate input
t = obj.t; % this time step
climate_in = obj.input_climate(t,:); % climate at this step
P = climate_in(1);
Ep = climate_in(2);
T = climate_in(3);
% fluxes functions
flux_ebs = evap_5(m,S1,sb,Ep,delta_t);
flux_eveg = evap_6(m,sfc,S1,sb,Ep,delta_t);
flux_qse = saturation_1(P,S1,sb);
flux_qss = interflow_7(S1,sb,sfc,a,b,delta_t);
flux_qr = baseflow_1(r,flux_qss);
flux_qb = baseflow_2(S2,a,b,delta_t);
flux_qt = flux_qse + (flux_qss-flux_qr) + flux_qb;
% stores ODEs
dS1 = P - flux_ebs - flux_eveg - flux_qse - flux_qss;
dS2 = flux_qr - flux_qb;
% outputs
dS = [dS1 dS2];
fluxes = [flux_ebs, flux_eveg, flux_qse, flux_qss,...
flux_qr, flux_qb, flux_qt];
end
% STEP runs at the end of every timestep
function [out] = evap_5(p1,S,Smax,Ep,dt)
%evap_5 evaporation based on scaled current water storage, for a fraction
%of the surface
% Copyright (C) 2019, 2021 Wouter J.M. Knoben, Luca Trotter
% This file is part of the Modular Assessment of Rainfall-Runoff Models
% Toolbox (MARRMoT).
% MARRMoT is a free software (GNU GPL v3) and distributed WITHOUT ANY
% WARRANTY. See <https://www.gnu.org/licenses/> for details.
% Flux function
% ------------------
% Description: Evaporation from bare soil scaled by relative storage
% Constraints: Ea <= Ep
% Ea <= S/dt
% @(Inputs): p1 - fraction of area that is bare soil [-]
% S - current storage [mm]
% Smax - maximum storage [mm]
% Ep - potential evapotranspiration rate [mm/d]
% dt - time step size [d]
out = max(min((1-p1).*S./Smax.*Ep,S/dt),0);
end
function [out] = evap_6(p1,p2,S,Smax,Ep,dt)
%evap_6 evaporation based on scaled current water storage, a wilting point,
%a constraining factor and limited by potential rate.
% Copyright (C) 2019, 2021 Wouter J.M. Knoben, Luca Trotter
% This file is part of the Modular Assessment of Rainfall-Runoff Models
% Toolbox (MARRMoT).
% MARRMoT is a free software (GNU GPL v3) and distributed WITHOUT ANY
% WARRANTY. See <https://www.gnu.org/licenses/> for details.
% Flux function
% ------------------
% Description: Transpiration from vegetation at the potential rate if
% storage is above a wilting point and scaled by relative
% storage if not
% Constraints: Ea <= Ep
% Ea <= S/dt
% @(Inputs): p1 - fraction vegetated area [-]
% p2 - wilting point as fraction of Smax
% S - current storage [mm]
% Smax - maximum storage [mm]
% Ep - potential evapotranspiration rate [mm/d]
% dt - time step size [d]
out = min([p1.*Ep,p1*Ep*S./(p2*Smax),S/dt]);
end
function [out] = saturation_1(In,S,Smax,varargin)
%saturation_1
% Copyright (C) 2019, 2021 Wouter J.M. Knoben, Luca Trotter
% This file is part of the Modular Assessment of Rainfall-Runoff Models
% Toolbox (MARRMoT).
% MARRMoT is a free software (GNU GPL v3) and distributed WITHOUT ANY
% WARRANTY. See <https://www.gnu.org/licenses/> for details.
% Flux function
% ------------------
% Description: Saturation excess from a store that has reached maximum capacity
% Constraints: -
% @(Inputs): In - incoming flux [mm/d]
% S - current storage [mm]
% Smax - maximum storage [mm]
% varargin(1) - smoothing variable r (default 0.01)
% varargin(2) - smoothing variable e (default 5.00)
if size(varargin,2) == 0
out = In.*(1-smoothThreshold_storage_logistic(S,Smax));
elseif size(varargin,2) == 1
out = In.*(1-smoothThreshold_storage_logistic(S,Smax,varargin(1)));
elseif size(varargin,2) == 2
out = In.*(1-smoothThreshold_storage_logistic(S,Smax,varargin(1),varargin(2)));
end
end
function [out] = interflow_7(S,Smax,p1,p2,p3,dt)
%interflow_7
% Copyright (C) 2019, 2021 Wouter J.M. Knoben, Luca Trotter
% This file is part of the Modular Assessment of Rainfall-Runoff Models
% Toolbox (MARRMoT).
% MARRMoT is a free software (GNU GPL v3) and distributed WITHOUT ANY
% WARRANTY. See <https://www.gnu.org/licenses/> for details.
% Flux function
% ------------------
% Description: Non-linear interflow if storage exceeds a threshold
% Constraints: f <= (S-p1*Smax)/dt
% S-p1*Smax >= 0 prevents numerical issues with complex
% numbers
% @(Inputs): p1 - storage threshold as fraction of Smax [-]
% p2 - time coefficient [d]
% p3 - exponential scaling parameter [-]
% S - current storage [mm]
% Smax - maximum storage [mm]
% dt - time step size [d]
out = min(max(0,(S-p1.*Smax)/dt),(max(0,S-p1.*Smax)./p2).^(1/p3));
end
function [out] = baseflow_1(p1,S)
% baseflow_1
% Copyright (C) 2019, 2021 Wouter J.M. Knoben, Luca Trotter
% This file is part of the Modular Assessment of Rainfall-Runoff Models
% Toolbox (MARRMoT).
% MARRMoT is a free software (GNU GPL v3) and distributed WITHOUT ANY
% WARRANTY. See <https://www.gnu.org/licenses/> for details.
% Flux function
% ------------------
% Description: Outflow from a linear reservoir
% Constraints: -
% @(Inputs): p1 - time scale parameter [d-1]
% S - current storage [mm]
out = p1.*S;
end
function [out] = baseflow_2(S,p1,p2,dt)
%baseflow_2
% Copyright (C) 2019, 2021 Wouter J.M. Knoben, Luca Trotter
% This file is part of the Modular Assessment of Rainfall-Runoff Models
% Toolbox (MARRMoT).
% MARRMoT is a free software (GNU GPL v3) and distributed WITHOUT ANY
% WARRANTY. See <https://www.gnu.org/licenses/> for details.
% Flux function
% ------------------
% Description: Non-linear outflow from a reservoir
% Constraints: f <= S/dt
% S >= 0 prevents numerical issues with complex numbers
% @(Inputs): S - current storage [mm]
% p1 - time coefficient [d]
% p2 - exponential scaling parameter [-]
% dt - time step size [d]
out = min((1./p1*max(S,0)).^(1./p2),max(S,0)/dt);
end
function [out] = smoothThreshold_storage_logistic(S,Smax,r,e)
%smoothThreshold_storage_logistic Logisitic smoother for storage threshold functions.
% Copyright (C) 2018 Wouter J.M. Knoben
% This file is part of the Modular Assessment of Rainfall-Runoff Models
% Toolbox (MARRMoT).
% MARRMoT is a free software (GNU GPL v3) and distributed WITHOUT ANY
% WARRANTY. See <https://www.gnu.org/licenses/> for details.
% Smooths the transition of threshold functions of the form:
%
% Q = { P, if S = Smax
% { 0, if S < Smax
%
% By transforming the equation above to Q = f(P,S,Smax,e,r):
% Q = P * 1/ (1+exp((S-Smax+r*e*Smax)/(r*Smax)))
%
% Inputs:
% S : current storage
% Smax : maximum storage
% r : [optional] smoothing parameter rho, default = 0.01
% e : [optional] smoothing parameter e, default 5
%
% NOTE: this function only outputs the multiplier. This needs to be
% applied to the proper flux utside of this function.
%
% NOTE: can be applied for temperature thresholds as well (i.e. snow
% modules). This simply means that S becomes T, and Smax T0.
% Check for inputs and use defaults if not provided
% NOTE: this is not very elegant, but it is more than a factor 10 faster then:
% if ~exist('r','var'); r = 0.01; end
% if ~exist('e','var'); e = 5.00; end
if nargin == 2
r = 0.01;
e = 5.00;
elseif nargin == 3
r = r{1};
e = 5.00;
elseif nargin == 4
r = r{1};
e = e{1};
end
% Calculate multiplier
Smax = max(Smax,0); % this avoids numerical instabilities when Smax<0
if r*Smax == 0
out = 1 ./ (1+exp((S-Smax+r*e*Smax)/(r)));
else
out = 1 ./ (1+exp((S-Smax+r*e*Smax)/(r*Smax)));
end
end
Note
This standardized MARRMoT structure is not identical to the original named model. p01... follow exact source order; s01... are fixed initial stores, defaulting to zero. Octave + optim are required. Solver behavior can differ across runtime versions.
Simulation
from basinforge import Basin, get_model
basin = Basin.from_csv("basin.csv", basin_id="A", area_km2=1200,
q_unit="m3/s", timestep="daily")
q_mm = get_model("MARRMOT_09").simulate(basin)
q_m3s = basin.to_m3s(q_mm)
Supply your actual data and catchment area; temperature-dependent models require a temperature column. For non-daily models, choose an appropriate warmup in model steps.
See calibration, input requirements, sources and verification limitations.