SNTEMP (In)Frequently Asked Questions: Maximum and Minimum Temperature Issues

Q2. 1. In SSTEMP, when you speed up the water velocity, the maximum temperature INCREASES. How come?

2. When you vary the day length (this is probably cheating), the maximum water temp decreases as day length increases. Why?

A2. 1a. I’m not sure what you were doing to "increase the velocity", but what I did to test this was to increase the slope by changing the upstream elevation. When you do so, the convective cooling decreases slightly (I’m really not sure why, probably because the depth decreases), but what really makes the difference is an increase in the friction component of the heat flux. I’m not sure I really believe this, but this is what the model shows. I do know that if you increase the slope to very unrealistic values, you can actually boil water, which I know I don’t believe. This is where the "all things being equal" clause goes out the window. Take a steep headwater situation for example. The gradient may be steep, but the "stream" is really very wide and composed of rivulets instead of being confined. Also, small waterfalls tend to increase the air-water interface "width", so evaporative cooling takes over instead of friction.

1b. If you increased the velocity by decreasing Manning’s n, then once again the depth decreases with the same amount of flow. This changes the heat flux components –look in the lower right corner of the screen to see what changes. Yes, it seems counterintuitive to me too.

2. All other things being equal bites again. Increasing the daylight hours, while leaving the solar radiation alone, means that the radiation is not as intense for any given hour. Thus the maximum goes down. This one is relatively easy to intuit. [Added 12/2001]

Q78. I was pestering you a couple of years ago about a heat flux printing problem, which resulted in SSTEMP versions 3.8 and 3.9. I’ve been using SSTEMP recently, and have had the "necessity" of using a Manning's n of 1.5. I came to this value in forcing the depth to agree with cross section data at my flow site. It also has the fortuitous effect of putting the maximum temperature predictions in nearly perfect agreement with measured maximums. The stream has a slope of 0.0033, is 42 ft wide, flow at time of modeling=12.4 cfs, 0.7 ft deep at my flow site, very sinuous, and almost perfectly rectangular (B term = 0). The reaches I am modeling are between 4.1 and 2.8 miles long. I'm confused at how I reached such a high n? The channel itself is a cobble gravel stream, with mostly glides. Is the high n an artifact of my forcing the depth to agree with an unrepresentative flow site; i.e. pools are not accounted for, and average depth is really greater? I fear I may be in a loop of circular reasoning, and would appreciate your experience in this matter. I’m using the same values for four consecutive reaches with similarly great results. However, the literature for the SSTEMP model says that values of n between 1 and 1.5 create instabilities in the model. 1) What kind of instabilities are you referring too? 2) Is the high n value I employ totally off the wall?

A78. The instabilities in SSTEMP occur simply because the artificial breakpoint of changing systems of units within the program, with 1.0 being the breakpoint in going from Manning’s n to travel time in seconds per kilometer or mile. It gets screwy sorting out exactly which system of units one is in (without the user explicitly so stating). Bottom line is that if the model is showing about the right depth and giving good results for maximum temperatures, then all is well. Just don’t start swapping units too much - - and keep an eye on it. [Added 12/2001]

Q79. Is the relatively (to those in published literature: i.e., Keith Richards "Rivers" 1982) high n I use an artifact of reaches that are shorter than the likely travel time? My four reaches are between 4.5-6.5 km in length, and travel times extrapolated from my flow site average velocities are around 6.5 to 14 km/day for the August time period addressed by the model. You mention this as a problem in the supporting literature, discussing single or multiply day averages, but I’m not sure if this is how it is manifested; or whether I have made some other compensating error.

A79. For what it’s worth, I have recently become interested in how much of the true stream flow may be traveling underground, something that is difficult to tell. But if large portions of the apparent flow were underground, this too would simultaneously increase Manning's n and dampen the maximum daily water temperature. The only way to really tell this, I think, would be to compare the flow at a bedrock control with stream flows in other portions of the channel. Or perhaps actually do a dye study to see what the true travel time is - - but you might have to measure for a long time to get the complete tail of the dye. [Added 12/2001]

Q80. Why does increasing n, and time of travel, in SSTEMP lower the predicted value of maximum temperature? Both factors increase time of exposure to incoming heat flux (I assume), which should increase the maximum temperature of the water.

A80. For your situation, I’m not sure what to recommend. Having a Manning’s of 0.8 will likely raise some eyebrows, as it should. You should deflect criticism by pointing this out and saying that it raises the possibility that predictions of maximum temperature may not be valid outside the range of calibration. Alternately, you could split your data set into situations least like and most like those you wish to make management predictions for. Then calibrate for the "least like" set and see how well the model does with the "most like" set. If the model does well, that increases your confidence. Then combine data sets, recalibrate (which you actually already have done) and you’re off and running. If the model doesn’t validate well with the "most like" you’re stuck I suppose, and must retreat to some external (regression?) model for maximum temperatures that must be similarly validated. [Added 12/2001]

Q88. Theurer used Manning's equation to estimate the mean depth of each flow segment, and then estimate the mean water velocity, both of which are important in calculating maximum daily water temperature. The depth controls the mass of water that must be heated (or cooled) and the velocity controls the exposure time for water that is exposed to heat flux from the mean daily temperature to the maximum daily temperature.

From Richards (1982) page 63, the well-known Manning's equation is:

SSTEMP has input for flow (width*depth*velocity) and width, but depth and velocity are undefined, hence:

1) How can Theurer to use n to determine R (depth) and travel time (1/v), since they comprise two unknown variables in the above equation?

2) Since we can, in some situations, readily measure average depth in a reach, but never n, could there be a option developed in SSTEMP to input depth when it is known, and since all the other variables except n would then be defined, n could be precisely determined.

A88. 1. As I understand it, Manning's equation was developed to empirically describe water's behavior in a trapezoidal, concrete-lined, open canal. Its utility was apparent in modeling free-flowing streams and rivers, particularly at flood flows, when and if those systems are "well behaved". Obviously, the less well behaved a stream is, the less Manning's equation could be expected to work.

2. Manning's n is an aggregate value that describes the full complement of channel roughness, ranging from small-scale edge and substrate effects to larger-scale channel morphological and bedform characteristics. Some people estimate the slope of the energy gradient as the water surface slope, or bed slope if that is the only info available. Others use the energy slope and will sometimes approximate (assume) the energy slope is the same as the water surface slope. a few will use the bed slope but only with long distances between cross sections. Neither is entirely correct, but "work" for many applications.

3. Many things can go "wrong" with Manning's equation in real-world applications. First, it is expected that Manning's n will vary as a function of flow, commonly portrayed as n = a * Q ^ b, but without careful measurement, we do not know these parameters a priori. The equation above is mostly applicable to gravel/cobble bed rivers. Sand-bed channels have their own set of equations. Also, many things, like odd channel obstructions (e.g., logs fallen across the channel) can cause non-linearity in the otherwise useful relation shown above.

4. It is likely that, given the above considerations, Manning's equation is really not appropriate in your relatively low flow channel with a lot of heterogeneity of pools, riffles, and runs. The energy slope is not likely to be well represented by the upstream and downstream elevations given the intervening pools.

5. Theurer used Manning's equation to estimate the mean depth of each flow segment, and then estimate the mean water velocity, both of which are important in calculating maximum daily water temperature. The depth controls the mass of water that must be heated (or cooled) and the velocity controls the exposure time for water that is exposed to heat flux from the mean daily temperature to the maximum daily temperature.

(At Theurer's suggestion, and with Bob's help, I added the travel time replacement for Manning's n.) It is the relative ratio of depth to time that seems to control how Manning's n (or travel time) will effect the maximum temperature. Under some conditions, increasing n may increase the maximum temperature, and under other conditions the opposite may be true.

6. Regardless of all the theoretical problems, I still think that using a high Manning's n in either SNTEMP or SSTEMP could be acceptable. Its use reflects Theurer's intention of capturing the appropriate mixing depth and travel time, i.e., the parameter may do what it is supposed to do even if it is no longer truly a Manning's n value. It becomes instead a "fudge factor"; in fact, let's call it the "depth-time factor" instead of Manning's n.

Having said that however, since your travel times (6.5 to 14 km per day) are large compared to the segment length (4.5 to 6.5 km), you are violating one of the fundamental assumptions of the model, namely that water must flow from top to bottom in one time step. In situations where yesterday is pretty much like today and tomorrow, you will be fine, but when large day-to-day changes occur, the model may be expected to work less well. Perhaps this explains why you are getting R-squared values of 0.89 rather than 0.95.

7. Given the uncertainties, it would be wise to "validate" the model for flow conditions like those for which you wish to make management predictions. Then, if it works ok, recalibrate with the full data set as I mentioned in an earlier message.

8. P.S. In reviewing the source code for SNTEMP and SSTEMP, I noticed that Theurer (or whoever coded the model) used 0.6 as the exponent in Manning's equation instead of the more correct 2/3. I don't think this is a big deal, but did want to point it out. [Added 12/2001]

Q125. I am working on an SSTEMP modeling project. I thought I read somewhere that if prediction of the maximum daily water temperature was the important factor (more important than the daily mean value), then a relative humidity more typical to daytime hours could be used instead of an average 24-hour relative humidity. I am now receiving comments on the project and can't seem to find that written anywhere. Did I make it up? Should you always use the 24-hour relative humidity number? In my area I can usually find hourly relative humidity.

A125. The idea of using values more representative of maximum conditions has been discussed on occasion, but has never been tested. Because the theory of the model requires 24-hour averages (with the single exception of maximum daily air temperature in the Windows version of SSTEMP; are you using that version?) only 24-hour values are "sanctioned" at this point.
I wonder if maybe you are thinking about my rule of thumb for relative humidity of multiplying the mean values by 1.2 as more representative of "at water's surface" conditions? I have found that doing this usually improves the fit for mean daily water temperatures, and I assume for maximum temperatures as well, but I haven't actually looked at that. [Added 6/2002]

Q126. The model is calibrated for mean temperature. Do you have any suggestions or insights to calibrating for Max temperature. The model results over predict the peak and valleys on our max temps. Is there a way to dampen the predictions (reduce the root mean square error, which is 1.37°).

A126. Here is an excerpt from somewhere:

Both the SSTEMP and SNTEMP models suffer from the disadvantage of less than perfect maximum temperature predictions. SNTEMP was developed to predict mean daily temperatures; the entire mathematical basis was simplified for this purpose. Maximum daily temperature estimation was perhaps something of an afterthought and suffers from the following problems:

a. The calculations are empirical, not theoretical. It is a matter of coaxing an instantaneous maximum temperature out of a daily average model. Theurer et al. (1984, pages II-30 to II-32), derive a way to estimate average afternoon air temperature, the major component of estimating maximum daily water temperature. Regression coefficients were determined for normal meteorological conditions at 16 selected weather stations around the country. (Normal has a specific meaning in this context. It is the arithmetic mean of a historical data set, usually represented by the previous 30-year period.) Table II-3 (in Theurer et al. 1984) shows the R-values, standard deviations, and probable differences for each of the 16 stations and for all stations combined. Each of these three statistics is noticeably poorer for all stations combined than for most of the individual stations. This means, no surprise, that we are not sampling from the same underlying distribution in creating the coefficients for the whole set. This is evident in the regression coefficients (a0, a1, a2, and a3), which are highly variable, often by an order of magnitude, as well as varying from positive to negative. This can be improved by performing the same regression for your local study area's meteorology. There is a provision to substitute your own coefficients in the job control file. Note that SSTEMP has been improved to allow you to supply the maximum daily air temperature.

b. Updating the regression coefficients, however, is not likely to fully correct the maximum daily water temperature calculations in areas within about six hours travel time from either reservoirs or major tributaries with markedly different mixing temperatures. The reason is that SNTEMP doesn't "know" anything about upstream conditions in predicting maximum temperatures. The program extends the current reach's stream geometry "indefinitely" upstream to simulate the conditions through which the water must travel from solar noon (assumed mean daily water temperature) to solar sunset (assumed maximum daily water temperature). This in itself is a major limitation of the model, only partially corrected in the SSTEMP program by the addition of the Dam at head of segment switch.

c. The distance the model looks upstream to find the water at solar noon is a function of flow, width, and Manning's n, all of which are average values. Many people have a feel for Manning's n values only by experience with one of the Fort Collins Science Center hydraulic simulation models, IFG4. Such experience, however, may be misleading because the Manning's n values in IFG4 are really not hydraulic retardance values at all, but rather act as velocity adjustment factors - - a nice name for a fudge factor. Manning's n values derived from a water surface profile (WSP) type simulation are likely to be much more representative. Consultants from Woodward Clyde have told me that measurements of Manning's n from hydraulic simulations can be "very inaccurate" compared with actual measurements from time-of-travel studies. The fact that n or travel time both vary with discharge, especially at low flows, confounds the situation, and no provision is made in the models to do so. One could, of course, make multiple runs using different n values.

Each of the above reasons taken independently, and certainly combined, means that one should always treat the maximum daily water temperature predictions from SNTEMP with care and should subject the predictions to validation. It would be nice to enhance SNTEMP to directly enter readily available maximum daily air temperatures, but it has never been a high enough priority. [Show us the money.]

Corrections for the regression coefficients and Manning's n should both help. Neither, however, will eliminate the problem with "looking" upstream. This is an area for improvement in the programs. Indeed, Woodward Clyde Consultants have apparently made proprietary improvements to the maximum temperature algorithms by changing the way the model "remembers" what is upstream. Their improvements show better correspondence with observations (Voos, pers. comm.). Even with these changes though, the models leave something to be desired.

The bottom line is that if maximum temperatures from SNTEMP prove unsatisfactory with the incorporation of localized a0 to a3 coefficients, the development of a regression model that includes the mean daily water temperature and appropriate meteorological variables in a fashion similar to the approach outlined in Theurer et al. (1984) is in order. Standard statistical techniques for inclusion or exclusion of parameters should be done. Occasionally, innovative approaches will be required.

New note: There has been some interesting work on maximum daily temperatures downstream from constant release temperature reservoirs like on the Sacramento River by Cindy Lowney and Mike Deas. They have found "nodes" of minimum diurnal temperature variation at multiples of a day's travel time downstream at the mean water velocity. See http://my.engr.ucdavis.edu/~wremg/sacto/sacexec.html for more. SNTEMP will not reproduce this phenomenon because of the empirical nature of the maximum temperature calculations. [Added 6/2002]

Q127. For some of our river nodes, the simulated average and maximum temperatures are equal. I'm wondering what may be causing this. Is it possible that travel time must be greater than some threshold value for there to be a difference between average and maximum temperatures? Our segment lengths are generally pretty short (0.1 to 0.5 km) and I'm thinking that this may be relevant.

A127. Good question. Internal S nodes are rarely used (by me anyway) so I don't know much about what's happening there, but I think I can speculate pretty well. SNTEMP does not attempt to simulate thermal processes in reservoirs. That's why you may choose only one of three types: a "regular" S node, a flow-through type, or an equilibrium release. For the flow-through type, temperature out equals temperature in. The equilibrium type release calculates equilibrium temperatures and then dumps water with that temperature as if the water came "off the top". And you specify the temperature for the regular release as if it were a deep-water release. For this deep-water release, the assumption is that the maximum temperature equals the mean daily temperature. I assume this is actually true for each of the three S node types, but have not verified that; it could be smarter than I think and either pass the upstream maximum through in the case of a flow-through S node or compute the maximum daily equilibrium in the case of an equilibrium release S node. Pretty easy to test in any case.

Unfortunately, the "features" of an S node stop at the structure because SNTEMP does not look back upstream from any node below the S node to see that there is indeed an S node up there. Because of this, maximum temperatures immediately downstream can be quite different from those at the preceding S. (Note that SSTEMP partially fixes this problem.) In your case, that appears to not be true, which seems odd and I'm not sure I can explain that. It may be possible to adjust travel time or Manning's n to get some leverage, but I'm not sure. How about seeing if Manning's n has an effect and let me know.

P.S. It turned out that there was actually another error that caused the bulk of this problem, but I thought the interchange contained valuable information regardless. [Added 6/2002]

Q220. Regarding Pg. 73, 3.b.4. Maximum Temperature; The limitations of predicting maximum daily water temperature with SNTEMP, in the IF 312 class notes, would it be possible to just use SSTEMP by segment to accomplish this? I guess it's obvious I've got an aversion to math? In addition, the Theurer reference you gave, II 30-32, seemed to address only air temperature? Maximum. daily water temperature, in association with hydropeaking operations is one of the most important issues I am facing.

A220. SSTEMP is slightly more precise on maximum temperatures than SNTEMP, but not necessarily with peaking. As above, if you really need maximum daily temperatures, it might be best to use a different model with a finer time step. Expect to pay royally however, as the data collection is a far larger effort.

Q221. I am modeling summer temperatures using SNTEMP for a reach of the X. River downstream of a reservoir that has a hypolimnetic cold water release. The entire reach I am modeling has a 1-day travel time and I am using a daily time step. I provide the model with starting mean daily water temperatures at the most upstream node (S node) located immediately downstream of the reservoir. As expected, I get very good results for mean daily predicted temperatures at this node. Since the model is “blind” to the upstream reservoir, the predicted maximum daily temperatures are high relative to the observed temperatures. I tried forcing the maximum daily temperature by assigning a very low width coefficient that would cause the channel to be artificially extremely narrow for this first S node but this did not help force the maximum lower. Do you have any suggestions on how to force the model to predict maximum daily temperatures identical to mean daily temperatures for a situation downstream of a hypolimnetic cold water release reservoir?
Follow-up - Setting the Manning's n to 0.9999 and setting the width coefficient to
0.1 gave me nearly identical mean daily and maximum daily temperatures.

(Question from me) Did you have to use these geometric attributes all the way downstream?
No, I was modeling a 19.1 km reach (1-day time step equals estimated 23 hour travel time at summer base flow - phew! Just long enough). Verification temperature data at 0.1, 8.9, 16.6, 17.7 and 19 km. The observed temperature pattern indicated the effect of the cold water release extended downstream as far as 16.6 km and beyond that temperatures were more or less in equilibrium with reach conditions. I backed off on the Manning's; .9999 for S node at head, then 0.5 ( for nodes between 19 and 17.7, then 0.45 down to 16.6 after which I could drop down to more traditional Manning's n values. Thanks for your interest and help

A221. Excellent question. I think about the best that can be done is to set Manning's n to 0.999. That will likely force the maximum to be very close to, but probably not identical to, the mean. You might also be able to adjust the so-called "a" coefficients and do even better. However, as you said, this is likely to work only for the first reach and may not carry through beyond that. You may need to carry this artificially high "n" further downstream. Try that and see what happens over a range of flows and meteorological conditions.

Q222. I'm finally getting around to actually writing up my thesis and am now trying to summarize how SNTEMP works. I want to make sure I'm describing the inner workings of the model correctly but I'm a little unsure how the maximum stream temperatures are calculated. I understand how the maximum air temperature and corresponding maximum relative humidity is obtained using the regression model described by equation II-58 in the user’s manual. I am then assuming that the maximum air temperature and relative humidity are used to obtain the equilibrium temperature for average daytime conditions (Tex) and first order thermal coefficient for daytime conditions (Kx) used in equations II-115, II-116. Is this right? It is not explicitly stated how maximum air temperature is used so I wanted to make sure I had the right idea.

A222. I think you have it well defined. The program really uses the same routine to calculate heat flux regardless of whether it is for mean or maximum. The only difference is whether it uses the user-supplied mean daily air temperature (adjusted for elevation) or the estimated maximum daily air temperature (likewise adjusted) -- and all the flux parameters that are dependent on those air temperatures.

Q223. One more question - In Northern Nevada, summer air temperatures can fluctuate as much as 30 degrees F from morning to afternoon. However, SSTEMP appears to be calculating a daily maximum that is only about 4 degrees F over the daily mean. Is this something to worry about for any potential applications in Northern Nevada? Should I use the "maximum air temperature option" realizing there is some uncertainty in SSTEMP's ability to predict maximum temperatures? If I use the "maximum temperature option", will SSTEMP assume a higher median air temperature value than is appropriate for our weather? FYI - Our state water quality standards are for daily maximums and not daily means, so it is really the maximum water temperature that I am most interested in.

A223. When you say that "SSTEMP appears to be calculating a daily maximum that is only about 4 degrees F over the daily mean." I assume you are referring to maximum air temperatures. If so, I would say that the maximum air temperature estimation algorithm isn't doing very good! This makes me want to ask two things: (1) are you sure you have good estimates for relative humidity? and (2) how do the predicted maximum water temperatures compare with and without using the default maximum air temperature?

Regardless, always treat SSTEMP's (and SNTEMP's) estimates of maximum daily water temperature as having higher uncertainty than the means. You may be able to calibrate the daily maximums using Manning’s n, or possibly by inputting your own daily maximum air temperature, but before you rely on such a calibration, make sure it holds up under a variety of circumstances of potential management interest. And if you do such a calibration, note that developing a rationale for doing so may be vulnerable to criticism.

Using the maximum temperature option does nothing to the mean daily air temperature.

If your interest is primarily in daily maximum water temperature, SSTEMP may not be the best model. Unfortunately, alternatives are hard to come by and more expensive to develop and use.

Q224. Thanks for your responses over the past few weeks. Despite the fact I have tried to figure out how Manning’s n “behaves”, through the FAQs and other sources, I still can’t quite get a handle on how changing the values for Manning’s n affects the maximum temperature. My understanding was/is that Manning’s n is a roughness coefficient, and therefore, theoretically, when one lowers the Manning’s n a stream should “move” faster. Wouldn’t this decrease temperature? However, in SNTEMP when I decrease the Manning’s n, the predicted temperature from SNTEMP increases. I read the explanation for this in the FAQs: Maximum and Minimum Temperature Issues (i.e. Manning’s n is used to get at depth, and when Manning’s n decreases, depth decreases and this results in higher temperatures). So, I guess my question is this: Is Manning’s n used in SNTEMP exclusively to get at depth, as opposed to being used in the manner of a “one to one” relationship with water temperature (i.e. as Manning’s decreases, velocities increase and therefore temperatures decrease)? I have a feeling this is all due to the fact flow does not change. I hope this makes sense.

A224. You are indeed on the right track. If we for the moment ignore the "travel time" option in SSTEMP, Manning's n shows up in the code for both models in Manning's equation:

where the FrictionSlope is simply the reach's gradient. But because velocity (m/sec) can be computed by dividing the discharge (m3/s) by m-wide and m-deep, and Manning’s N controls the depth, N influences velocity and therefore exposure time. But depth (and width) is quite sensitive for maximum temperatures because this controls the cross-sectional volume that in turn controls what many refer to as "thermal inertia". I don't really like this term, but must admit that it is descriptive. Said another way, Manning’s N then controls not only velocity (and exposure) but also depth (and width) and is therefore not a truly independent parameter as the models are currently formulated.

SSTEMP does go the extra mile (literally) in more accurately calculating travel time (and therefore exposure time) for a parcel of water to reach the downstream boundary of the reach under consideration and predict the maximum daily water temperature -- if there is a dam at the upstream boundary. SNTEMP does not make the same calculation, so maximum daily water temperatures are more approximate in this model. The maximum temperature prediction in both models is only an approximation, even with the slight improvement in SSTEMP.

NOTE: I (and others) have used Manning’s N to "calibrate" certain reaches below dams with some success, but I will always caution people to be wary of doing so especially if the results are to be extrapolated far beyond the calibration range.

Q225. I am calibrating the model right now, and I have read the FAQs on using Manning's n values. In particular, the use of high values to reduce simulated maximum temperatures; in effect making Manning's n more of a fudge factor. So, the question really is this.... how high of a value is reasonable? I saw in the FAQs where some folks have used values of .10 to .15. Is there a point beyond which a value is just not reasonable?

What I would want to do is to get a feel for how N influences maxima at a "low" flow and at a "high" flow. Now, depending on your objectives, you may only be interested in accurately predicting maximum temperatures at low flows. If so, adjust N explicitly for these occasions with an eye toward how doing so may make predictions at "high" flows less accurate. Then you may be able to build up enough experience to say that your model works best at flows roughly up to some specified level and then becomes less accurate. Such knowledge is probably better than adhering to any specific acceptable range for N since, as you have said, the parameter is being used as a fudge to account for inaccuracy in the model.