general_functions Module Reference

Functions/Subroutines
real function, public	tempfactor (temp)
real function, public	halfsatconcfactor (conc, par)
real function, public	moisturefactor (sm, wp, pw, thickm, satsmf, exp, thetalow, thetaupp)
real function, public	exponential_moisturefactor (sm, pw, limpar, exp)
real function, public	simple_rating_curve (wst, k, p, w0)
real function, public	exponential_decay (timesteps, halflife)
subroutine, public	sedimentation (depth, conc, vel, lim, delta)
real function, public	plant_growth (up1, up2, up3, day)
real function, public	sigmoid_response (x, xs, xe, ys, ye, xm)
real function, public	linear_response (x, xs, xe, ys, ye)
real function, public	water_density (t, s)

Detailed Description

General equations that are used by hydrological models.

Function/Subroutine Documentation

exponential_decay()

real function, public general_functions::exponential_decay	(	real, intent(in)	timesteps,
		real, intent(in)	halflife )

Calculates fraction left after exponential decay with a half-life parameter.

Parameters

[in]	timesteps	in unit of half time
[in]	halflife	half-life of decay

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exponential_moisturefactor()

real function, public general_functions::exponential_moisturefactor	(	real, intent(in)	sm,
		real, intent(in)	pw,
		real, intent(in)	limpar,
		real, intent(in)	exp )

Calculates an exponential soil moisture dependence factor.

Parameters

[in]	sm	soil moisture (mm)
[in]	pw	total pore wolume (mm)
[in]	limpar	limitation parameter of moisturefactor (mm)
[in]	exp	exponent of moisturefactor

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halfsatconcfactor()

real function, public general_functions::halfsatconcfactor	(	real, intent(in)	conc,
		real, intent(in)	par )

Calculates a concentration dependence factor Based on: half saturation function.

Parameters

[in]	conc	current concentration
[in]	par	half saturation concentration

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linear_response()

real function, public general_functions::linear_response	(	real, intent(in)	x,
		real, intent(in)	xs,
		real, intent(in)	xe,
		real, intent(in)	ys,
		real, intent(in)	ye )

Linear function between (xs,ys) and (xe,ye) y = ys + (ye-ys)/(xe-xs))*x with xs <= x < xe.

Parameters

[in]	x	input variable (e. snow depth, water level, temperature, etc)
[in]	xs	x value defining the start of the response function (for instance 0.)
[in]	xe	x value defining the end of the response function (for instance 1.)
[in]	ys	y value at the start of the response function (for instance 0.)
[in]	ye	y value at the end of the response function (for instance 1.)

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moisturefactor()

real function, public general_functions::moisturefactor	(	real, intent(in)	sm,
		real, intent(in)	wp,
		real, intent(in)	pw,
		real, intent(in)	thickm,
		real, intent(in)	satsmf,
		real, intent(in)	exp,
		real, intent(in)	thetalow,
		real, intent(in)	thetaupp )

Calculates a soil moisture dependence factor.

Parameters

[in]	sm	soil moisture (mm)
[in]	wp	wilting point pore wolume (mm)
[in]	pw	total pore wolume (mm)
[in]	thickm	thickness of soil layer (m)
[in]	satsmf	saturated moisturefactor (satact)
[in]	exp	exponent of moisturefactor (thetapow)
[in]	thetalow	low(?) moisture coefficient (thetalow)
[in]	thetaupp	high(?) moisture coefficient (thetaupp)

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plant_growth()

real function, public general_functions::plant_growth	(	real, intent(in)	up1,
		real, intent(in)	up2,
		real, intent(in)	up3,
		real, intent(in)	day )

Calculates a logistic growth for plant based on a three-parameter equation from SOILN.

Reference: Eckersten, H., P.-E. Jansson, and H. Johnsson 1994. SOILN model - user's manual 2nd edition, Division of Agricultural Hydrotechnics Communications 94:4, Department of Soil Sciences, Swedish University of AgriculturalSciences, 58pp, Uppsala).

Parameters

[in]	up1	parameter 1
[in]	up2	parameter 2
[in]	up3	parameter 3
[in]	day	variable

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sedimentation()

subroutine, public general_functions::sedimentation	(	real, intent(in)	depth,
		real, intent(in)	conc,
		real, intent(in)	vel,
		real, intent(in)	lim,
		real, intent(out)	delta )

Calculate sedimentation from sinking velocity.

Parameters

[in]	depth	water depth (m)
[in]	conc	concentration of substance to sedimentate (mg/L or something)
[in]	vel	sinking velocity (m/timestep)
[in]	lim	concentration limit of sedimentation rate (mg/L or ?)
[out]	delta	sedimented amount (g/m2 or something)

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sigmoid_response()

real function, public general_functions::sigmoid_response	(	real, intent(in)	x,
		real, intent(in)	xs,
		real, intent(in)	xe,
		real, intent(in)	ys,
		real, intent(in)	ye,
		real, intent(in)	xm )

Flexible sigmoid function to approximate a response function (for instance a growth or depletion curve) with well defined parameters.

References: Yin et al., Annals of Botany 91: 361-371, 2003, doi:10.1093/aob/mcg029 Pimentel et al., Hydrol. Earth Syst. Sci., 21, 805-820, 2017

The original function by Yin et al is defined using xs=0 and ys=0:

y = ye * (1 + (xe - x)/(xe - xm))(x/xe)^(xe / (xe-xm)), with 0<= xm < xe

We can generalize this to have response y between ys and ye for input variable xs to xe:

y = ys + (ye-ys)*(1 + (xet-xt)/(xet-xmt))*(xt/xet)^(xet/(xet-xmt)), with xt=x-xs, xet=xe-xs, xmt=xm-xs, and xs <= xm < xe

Parameters

[in]	x	input variable (e. snow depth, water level, temperature, etc)
[in]	xs	x value defining the start of the response function (for instance 0.)
[in]	xe	x value defining the end of the response function (for instance 1.)
[in]	ys	y value at the start of the response function (for instance 0.)
[in]	ye	y value at the end of the response function (for instance 1.)
[in]	xm	x value with maximum slope of the response function (any value between xs and xe)

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simple_rating_curve()

real function, public general_functions::simple_rating_curve	(	real, intent(in)	wst,
		real, intent(in)	k,
		real, intent(in)	p,
		real, intent(in)	w0 )

Calculates momentanous flow from current water level with simple rating curve equation: Q = k*(w-w0)**p.

Parameters

[in]	wst	current water level (m)
[in]	k	rating curve coefficient
[in]	p	rating curve exponent
[in]	w0	rating curve threshold (m)

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tempfactor()

real function, public general_functions::tempfactor

(

real, intent(in)

temp

)

Parameters

[in]

temp

current temperature

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water_density()

real function, public general_functions::water_density	(	real, intent(in)	t,
		real, intent(in), optional	s )

Water density (kg/m3) as a function of temperature and salinity rho = rhoref * (1 - c1 * (T - Tref)^2 + c2 * S) Default equation from PROBE97 (except rhoref=1000).

Parameters

[in]	t	water temperature (degree Celsius)
[in]	s	water salinity (PSU)

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