Surface energy balance and water balance - understanding the equations
Radhakrishna BL
Radhakrishna BL
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Coon, Ethan
See below, my text in red.
Ethan
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Ethan Coon
Senior Research Scientist
Oak Ridge National Laboratory
https://www.ornl.gov/staff-profile/ethan-t-coon
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From:
ats-...@googlegroups.com <ats-...@googlegroups.com> on behalf of Radhakrishna BL <radhakri...@gmail.com>
Date: Thursday, October 20, 2022 at 3:30 AM
To: Amanzi-ATS Users <ats-...@googlegroups.com>
Subject: [EXTERNAL] Re: Surface energy balance and water balance - understanding the equations
Dear ATS Users,
A gentle reminder about the questions.
Thank you.
On Fri, 14 Oct 2022 at 16:29, Radhakrishna BL <radhakri...@gmail.com> wrote:
Dear ATS-Users,
I currently have cases (with and without snow) that consider the following processes: Subsurface flow and energy with ice content + Overland flow and energy with ice content + Surface energy and water balance. I have a pseudo-1-D model of 40 m depth with three layers. Here are the questions:
1. The equation for the emissivity of air (to calculate incoming longwave radiation(Atchley 2015):
Is it the same equation also used in the ATS 1.2 version? And is it (I) .. (0.01ea)^(Ta/2016) or (ii) (0.01ea)*(Ta/2016)
This hasn’t changed in a long while, and probably not since the paper. You’d have to look at the code to be sure – this should be in src/pks/surface_balance/constitutive_relations/land_cover/seb_physics_funcs.cc.
2. I have considered Delta T as one day (daily time step). For the surface water balance, the precipitation (rain and snow) has been considered in meter second^{-1}. Is it internally converted by ATS to m day^{-1} and added above?
No. Internally, the code always works in seconds, no matter what you set the required times or any other time unit to. So all fluxes, both inputs and outputs, are in “/s” units. The one exception to this is any observation where you use the “integrated in time” option, which then is “per observation increment” in whatever increment you provide for the observations.
3. I have considered 'region: boundary' as the surface outlet. How does the water then exit the system? Is the discharge (mentioned below) the total amount of water moving out of the system from the surface?
Having a region is not enough for there to be discharge. You must also provide a boundary condition on that region that allows outflow across that region. See for instance the ats-regression-tests repository, under 03_surface_water, where there are boundary conditions discussed for overland flow, or the input spec documentation that describes the flow BCs.
Once you’ve set a boundary condition, this observation will then integrate the water flux out of the domain across that region, in mol/s.
4. For the surface water balance: we have Q_water = S_r + P_r (Q_water is the total water flux, S_r is the sublimation/condensation rate, and P_r is the precipitation rate). Can we consider that the surface runoff is subtracted from the total water flux to calculate water infiltration into the subsurface?
No, because there may be changes in surface water storage. The global surface water conservation equation is:
dWC_surface/dt = P – E + SM – D – I
P = precip, E = evap/condens, SM = snowmelt, D = discharge, I = infiltration. I believe there is a detailed discussion of this in: https://github.com/amanzi/ats/blob/master/tools/utils/mass_balance.py
Or how does the surface-subsurface coupling work concerning water fluxes? Do we need to consider a subsurface storage term?
The surface-subsurface coupling works by ensuring continuity of both pressure and flux. See Coon et al AWR 2020 for details. Infiltration is written as “surface-subsurface_water_flux” and is in mol/s. You don’t need to consider subsurface storage for a mass balance on the surface, but obviously you do for the subsurface. See the above python script & documentation there for details.
5. Please let me know if I have understood the following variables the right way:
a. surface-thaw_depth: Vertical distance between the surface and the topmost cell where the temperature is at or below 0°C (Probably the temperature below this topmost cell also has to be below 0°C?).
yes, I think that is right. It may be the distance between the surface and the topmost cell where the saturation of ice is non-zero though, which is slightly different in most runs, but close enough.
b. surface-water_table_depth: Vertical distance between the surface and the topmost cell where it is fully saturated.
yes
c. surface-surface_subsurface_flux: The total mass (of water) flux entering the subsurface (infiltration).
yes
d. surface-ponded_depth: the amount of water depth that accumulates on the surface.
yes
e. surface-incoming_shortwave_radiation: Are these the same values as the input dataset - incoming shortwave radiation? or calculated by (1-alpha)*(incoming shortwave radiation)? Where alpha is the dynamic surface albedo?
Same as the input. Albedos are saved separately in their own variable, so you can get those as well.
6. The sign convention for water and heat flux variables: +ve is upwards (out of the surface-subsurface system). Is this right? Or does it change for water and heat flux variables?
For most variables, positive indicates heat or mass moving into the domain. The exception is the surface-subsurface_{water,energy}_flux variables, which are positive to the surface, or out of the subsurface. There may be a few other variables like that – it can be a bit tricky to keep track. One of my documentation goals is to have a table of variable names and descriptions that include sign conventions. Anyone wanting to take that on would be greatly appreciated!
7. I wanted to close the water balance and therefore convert the units of mass-related variables. y kg day^{-1} = [(18.02 g mol^{-1}*86400 s day^{-1} )/1000 g kg^{-1}] * x mol s^{-1}
I would recommend closing water balance in mols, like the code, rather than in kg. This becomes important when you get into systems involving transport and/or reactions (e.g. saline systems), and mols are the units that ATS actually conserves. Again, see the above python script for more.
8. What changes were made in the equations for ATS 1.2 compared to the model used in Atchley 2015?
1.2 changes a bunch of things, and 1.3 changes even more (coming very soon). Mostly 1.2 does not change equations, but does change conceptualization, in that we more cleanly define sub-sets of any given surface cell and solve the surface energy balance independently on each area. Think “half of my grid cell is water, half is not, so solve two equations and perform a weighted sum of the two areas to compute the total evaporation.” This is not currently published. 1.3 further changes some of the empirical terms, particularly in latent and sensible heat exchange as a function of wind speed, etc.
Best Regards,
Radhakrishna. B.L.
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Best Regards,
Radhakrishna.B.L.
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Radhakrishna BL
I checked, it is still the same.
2. I have considered Delta T as one day (daily time step). For the surface water balance, the precipitation (rain and snow) has been considered in meter second^{-1}. Is it internally converted by ATS to m day^{-1} and added above?
No. Internally, the code always works in seconds, no matter what you set the required times or any other time unit to. So all fluxes, both inputs and outputs, are in “/s” units. The one exception to this is any observation where you use the “integrated in time” option, which then is “per observation increment” in whatever increment you provide for the observations.
Suppose, I impose 10^{-7} m/s rainfall as the top boundary condition for a daily time step, How much is the amount of mass/rainfall that is applied as Top B.C every day? Is it 10^{-7} m/s? or 10^{-7} m/s * 86400 s/day? I am sorry I ask again.
3. I have considered 'region: boundary' as the surface outlet. How does the water then exit the system? Is the discharge (mentioned below) the total amount of water moving out of the system from the surface?
Having a region is not enough for there to be discharge. You must also provide a boundary condition on that region that allows outflow across that region. See for instance the ats-regression-tests repository, under 03_surface_water, where there are boundary conditions discussed for overland flow, or the input spec documentation that describes the flow BCs.
Once you’ve set a boundary condition, this observation will then integrate the water flux out of the domain across that region, in mol/s.
4. For the surface water balance: we have Q_water = S_r + P_r (Q_water is the total water flux, S_r is the sublimation/condensation rate, and P_r is the precipitation rate). Can we consider that the surface runoff is subtracted from the total water flux to calculate water infiltration into the subsurface?
No, because there may be changes in surface water storage. The global surface water conservation equation is:
dWC_surface/dt = P – E + SM – D – I
P = precip, E = evap/condens, SM = snowmelt, D = discharge, I = infiltration. I believe there is a detailed discussion of this in: https://github.com/amanzi/ats/blob/master/tools/utils/mass_balance.py
Or how does the surface-subsurface coupling work concerning water fluxes? Do we need to consider a subsurface storage term?
The surface-subsurface coupling works by ensuring continuity of both pressure and flux. See Coon et al AWR 2020 for details. Infiltration is written as “surface-subsurface_water_flux” and is in mol/s. You don’t need to consider subsurface storage for a mass balance on the surface, but obviously you do for the subsurface. See the above python script & documentation there for details.
5. Please let me know if I have understood the following variables the right way:
a. surface-thaw_depth: Vertical distance between the surface and the topmost cell where the temperature is at or below 0°C (Probably the temperature below this topmost cell also has to be below 0°C?).
yes, I think that is right. It may be the distance between the surface and the topmost cell where the saturation of ice is non-zero though, which is slightly different in most runs, but close enough.
b. surface-water_table_depth: Vertical distance between the surface and the topmost cell where it is fully saturated.
yes
c. surface-surface_subsurface_flux: The total mass (of water) flux entering the subsurface (infiltration).
yes
d. surface-ponded_depth: the amount of water depth that accumulates on the surface.
yes
e. surface-incoming_shortwave_radiation: Are these the same values as the input dataset - incoming shortwave radiation? or calculated by (1-alpha)*(incoming shortwave radiation)? Where alpha is the dynamic surface albedo?
Same as the input. Albedos are saved separately in their own variable, so you can get those as well.
6. The sign convention for water and heat flux variables: +ve is upwards (out of the surface-subsurface system). Is this right? Or does it change for water and heat flux variables?
For most variables, positive indicates heat or mass moving into the domain. The exception is the surface-subsurface_{water,energy}_flux variables, which are positive to the surface, or out of the subsurface. There may be a few other variables like that – it can be a bit tricky to keep track. One of my documentation goals is to have a table of variable names and descriptions that include sign conventions. Anyone wanting to take that on would be greatly appreciated!
7. I wanted to close the water balance and therefore convert the units of mass-related variables. y kg day^{-1} = [(18.02 g mol^{-1}*86400 s day^{-1} )/1000 g kg^{-1}] * x mol s^{-1}
I would recommend closing water balance in mols, like the code, rather than in kg. This becomes important when you get into systems involving transport and/or reactions (e.g. saline systems), and mols are the units that ATS actually conserves. Again, see the above python script for more.
8. What changes were made in the equations for ATS 1.2 compared to the model used in Atchley 2015?
1.2 changes a bunch of things, and 1.3 changes even more (coming very soon). Mostly 1.2 does not change equations, but does change conceptualization, in that we more cleanly define sub-sets of any given surface cell and solve the surface energy balance independently on each area. Think “half of my grid cell is water, half is not, so solve two equations and perform a weighted sum of the two areas to compute the total evaporation.” This is not currently published. 1.3 further changes some of the empirical terms, particularly in latent and sensible heat exchange as a function of wind speed, etc.
Best Regards,
Radhakrishna. B.L.
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Best Regards,
Radhakrishna.B.L.
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To view this discussion on the web visit hxxps://groups.google.com/d/msgid/ats-users/CAKcv5JMF-NWL0%2BLN1K37WHdTAWNXXk1A9hheaQbExhDKNno7Bg%40mail.gmail.com.
Coon, Ethan
I think the only question there is the rainfall rate clarification.
If you actually took a daily timestep, then the new mass would indeed be
1.e-7 [m/s] * dt [s] = 1.e-7 * 86400
Remember that most of our timestepping is adaptive timestepping, so it is unlikely that you are actually taking a daily timestep. You can set the max timestep, but often we will take smaller step sizes.
Radhakrishna. B.L.
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P = precip, E = evap/condens, SM = snowmelt, D = discharge, I = infiltration. I believe there is a detailed discussion of this in: hxxps://github.com/amanzi/ats/blob/master/tools/utils/mass_balance.py
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Best Regards,
Radhakrishna.B.L.
To view this discussion on the web visit hxxps://groups.google.com/d/msgid/ats-users/CAKcv5JMTLRMHMPV%2BsC82pWv490TUyyr8CiYOo01Jnwg2%3Df8taA%40mail.gmail.com.