SCS-CN method slope dependency

[jens]

It is documented in the SWAT theoretical manual that the SCS-CN method was developed for slopes of 5% (chapter 2.1.1.1). An equation exists to adjust these values according to the actual slope (chapter 2:1.1.1.4). CN-values for slopes <5% are reduced, for slopes >5% are increased. However, what I am finding in about 5% of my catchment area is the following: even after correcting the CN-values, runoff and erosion from steep HRUs (20-999%) is lower than from HRUs with same land use, same soil, but lower slope class (15-20%).

I can understand that, when looking at total subbasin or catchment yield, it might not matter much, because mild slopes are overestimated and thus can potentially level out this problem. However, when looking at soil and water conservation measures for different slope classes it can have an impact in my view.

I was wondering if anybody has observed something similar (particularly when applying SWAT in very steep regions)? Does somebody know some research that has gone into this particular slope dependency of the CN-values or the development of the CN-slope correction equation by Williams (1995)?

Thanks,

Jens

[Jim Almendinger]

Hmm, a similar problem of greater erosion from lesser slopes was brought up earlier this year, and I don't think we ever solved that problem.  

And, just to be clear to other readers -- SWAT does NOT automatically adjust CNs for slope, but the theoretical documentation gives an equation for the user to manually make the adjustment if desired.  

So -- you have more runoff and erosion from lesser slopes (for the same soils and land use).  Do you think this is consistent over all slopes (i.e., lower slopes always generate more runoff and erosion than steeper slopes), or does it only break down for steep slopes?  I.e., for gentle slopes (say, 0-20%?)  is there perhaps the expected positive relation between slope & runoff & erosion, but when steeper slopes are reached, the relation begins to reverse, with less runoff and erosion?  

Or -- are you finding that when you manually adjust CNs for steeper slopes (increasing them, e.g.), that you actually end up with less runoff and erosion than before you made the adjustment?  

I'd have to brush up on my SWAT theory, but I think there are a few calculations where SWAT does take into account the slope, such as calculating peak flow rate of runoff (maybe).  And I think slope is probably involved in calculating rates of lateral flow and storage within the soil layers (something I've never really understood).  I can only speculate that if SWAT is giving qualitatively wrong results that some of these equations may not be giving reasonable results when slopes become very steep.  Perhaps with lower slopes, lateral flow and percolation aren't enough to drain soil moisture, which then may impede percolation causing more runoff, compared to steeper slopes...  

Anyway, those are the areas where I'd start looking to solve the riddle. 

-- Jim

Dr. James E. Almendinger, Senior Scientist
St. Croix Watershed Research Station
Science Museum of Minnesota
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[R. Srinivasan]

Jim,
in ArcSWAT, we have an option to update the CN based on slope, so users can update the CNs based on hru slope.

Srini

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[jens]

Thanks for your answer, Jim!

I must have missed that earlier discussion in my search for similar posts. Probably you are referring to: https://groups.google.com/forum/?fromgroups=#!searchin/swatuser/erosion$20slope/swatuser/FB3s-r-hpus/PqRP_hptTkMJ
It could be that the problem Jamil describes is the same what I am experiencing.

Let me answer your questions first:
The relation breaks down for steep slopes. As you are describing, there is the expected positive relation between slope & runoff & erosion, but when steeper slopes are reached, the relation begins to reverse.
When I noticed that first, I thought it is due to the fact that I am NOT correcting the CN-values. After I corrected the CN values (an initial CN value from 80 becomes 76 for lowest and 84 for highest slopes), I ended up with more runoff and more erosion for the steepest slope class, but the phenomena of the reversing relation still exists.

In essence, it seems like, that in the project I am running, the correction of the CN-values does not seem to be "enough" or suitable for steepest slopes. I was wondering if there is more information out there on that.

When looking at erosion particularly (Jamils problem), there might be other factors besides the CN that play a role as well. Initially, the USLE was made for slopes of 9%, if I remember correctly. I never really found out if SWATs MUSLE is adjusted for different slopes...but I guess that issue would be a different thread.

Thanks again!
Jens

[jens]

JIM ALMENDINGER wrote:
Well -- this is very interesting, and unfortunately I don't see an easy way around the problem.  It appears that SWAT is not quite right at the steepest slopes.  My guess is that in most watersheds the steepest slopes are a small percentage of the basin, and so most users never notice the problem. 

In reading a bit on lateral flow, I noticed they use an approximation that may be part of the problem.  In the swat2009 theory manual, look at equations 2:3.5.7, where lateral flow velocity is related to Ksat and sin(hill slope).  They replace sin with tan in equation 2:3.5.8, since tan and sin are about the same for low slopes.  But at higher slopes the approximation breaks down.  Sin is limited to a maximum of 1, but at higher slopes, tan can far exceed 1 (and approach infinity).  I wonder if this approximation is a problem -- if lateral flow velocity is greatly overestimated at steeper slopes, does that mean that the surface soil layer is always well drained, and so runoff is much reduced?  It's just a guess, but it fits your pattern, that runoff and erosion are well behaved at low slopes, but start to go bad at steeper slopes. 

Unfortunately SWAT is complex enough it's hard to see all the possible causes, and it would take some time to explore more deeply.  If you have the time and can figure out anything more, let us know!  And thanks for identifying the problem. 

Cheers,
-- Jim


JENS' answer:
Thanks again for your mail and looking into this! First of all, I have to correct myself: Runoff sometimes already is lower in the higher slope class than the previous lower slope class even if we are not at max slope! But the problem is most distinct at the highest slope class.

However, you identified an interesting issue concerning the dependency of slope and lateral flow. Maybe, my hypothesis of the inappropriate CN-value correction equation is not a problem or not the only problem:

Have a look at equation 2:3.5.9: There, slp is proportional to Qlat. That means with higher slp, Qlat is higher (and might approach infinity if we have a vertical wall...!?). What is interesting, is the fact that Ksat is proportional in that equation too and I find the problem occurring most severe on soils with high conductivity.

I had a look in the code and, as far as I understand it, equation 2:3.5.9 is used to calculate lateral flow only if the soil layer is saturated (in the subroutine percmicro.f). Lateral flow is then subtracted from the soil water storage (in subroutine percmain.f). The daily CN is then calculated based on soil water storage (in subroutine dailycn.f). Now, equation 2:3.5.9 only has an impact on daily soil water storage (and ultimately on daily CN) if the water content is above field capacity. So I suspect, but I haven't checked, that this is the case in the HRUs and time steps at which the problem occurs (I am printing my results in monthly time steps and I don't want to go through the hustle of manually calculating field capacity and printing water content on HRU scale on daily time steps now).

What is interesting at that point is an option implemented in the code (in subroutine dailycn.f). There is an explanation in the manual (chapter 2:1.1.1.3): "An alternative method added in SWAT2009 allows the retention parameter to vary with accumulated plant evapotranspiration. (this) was added because the soil moisture method was predicting too much runoff in shallow soils". Though, the reasoning sounds different ("shallow soils") I gave it a go: I searched for the parameter that triggers this new option. It is ISN in .bsn (in ArcSWAT its a drop-down menu in "Edit General Watershed Parameters"). I ran my model again with ISN = 1 (Plant ET Method).

The results show that surface runoff has been changed considerably (in average by 50%). It has improved, but the problem is not totally solved. See the example:

CN-from soil moisture                                                 CN from ET

SLOPE	SURQ	SEDYLD		SURQ	SEDYLD
0-2	0.84802	0.00005		0.96972	0.00003
2-9	0.83330	0.00012		0.99100	0.00012
9-15	0.81337	0.00040		0.98680	0.00047
15-20	0.69963	0.00038		0.97802	0.00053
20-9999	0.41148	0.00020		1.00283	0.00052

Anyway, I let this issue go from here. It is exactly as you are saying: It is just too complex and too many factors might play a role. Thanks, Jim for your help here (and in various other posts to other users, which have helped me, too). I would have given up on this one. You really have a feeling for SWAT, thanks for sharing.

Best,
Jens

[jens]

Jim and I had additional discussions about this topic. Please find below our short summary of the issue. I have used Version rev.510 of the code.

(1) The soil-moisture CN method seems to give bad result for runoff on steeper slopes, with steeper slopes improperly having less runoff than gentler slopes. This may be related to SWAT using the tangent as an approximation for the sine of the slope, which affects lateral flow out of the soil layers, which in turn would affect the soil-moisture CN calculation. The CN-values correction equation according to slope can also play a (probably minor) role here.

(2) The plant-ET CN method seems to give better results for runoff on steeper slopes - at least in this current model. It leads to more plausible surface runoff values when comparing different slope classes.

(3) The two methods result in different water yields. In the current case, the plant-ET CN method resulted in a much larger water yield than the soil-moisture CN method (+50%). This might be due to high ET values (hot climate, irrigation). I used the Hargreaves ET Method.

The findings here might thus not be representative. If anybody can figure out something else or more, please let us know.

Thanks,
Jens

[Glenn Harwell]

How do we update the CN based on HRU slope? I see in the .mgt file there is a column for CN_SLOPE and the default value is 0. I can't find this parameter in the documentation. Does changing this to some number like 1 automatically update the HRU CN based on HRU slope?

[jens]

Hi Glenn,

in the past I had updated the CN-Values manually based on the equation by Williams (1995) (see Theoretical Manual Chapter 2).

But as Srini mentioned above, ArcSWAT has a box (in the edit management parameters menu) you can tick to do this for you. 

Cited from the ArcSWAT 2012 documentation:

"Note: If the “Adjust Curve Number for Slope” option is checked, the curve numbers specified in the general management and management operations will be adjusted to reflect the slope of the HRU using the equations found in Chapter 2 of the  Soil and Water Assessment Tool Theoretical Documentation, Version 2012. The adjustment is made to the curve numbers when printed to the .mgt ascii input files."

I have not checked the following, but according to the documentation, I assume that the CN_SLOPE column is written and read by ArcSWAT and if there is a 1, the CN-value of this particular HRU is corrected. So, if you change the CN_SLOPE value from 0 to 1 in the .mdb and rewrite your input files with ArcSWAT, your CN2 value in the .mgt file should change in case HRU slope is not 5%. CN_SLOPE is not a parameter of the .mgt file in the input files, which may have been the reason you could not find it in the docs.

Best

Jens