Uncertainty in Utah: Part 3 on The Hydrologic Model Data Set by Randall P. Julander

Uncertainty in Utah Hydrologic Data: Part 3 – The Hydrologic Model Data Set

 A three part series that examines some of the systematic bias in Snow Course, SNOTEL, Streamflow Data and Hydrologic Models

Randall P. Julander Snow Survey, NRCS, USDA


Hydrologic data collection networks and for that matter, all data collection networks were designed, installed and operated – maintained to solve someone’s problem. From the selection of sensors to the site location, all details of any network were designed to accomplish the purpose of the network. For example the SNOTEL system was designed for water supply forecasting and while it is useful for avalanche forecasting, SNOTEL site locations are in the worst locations for data avalanche forecasters want such as wind loading, wind speed/direction and snow redistribution. All data collection networks have bias, both random and systematic. Use of any data from any network for any purpose including the intended one but especially for any other purpose should include an evaluation for data bias as the first step in quality research. Research that links a specific observation or change to a relational cause could be severely compromised if the data set has unaccounted systematic bias.  Many recent papers utilizing Utah Hydrologic Data have not identified or removed systematic bias from the data. The implicit assumption is of data stationarity – that all things except climate are constant through time thus observed change in any variable can be directly attributed to climate change.   Watersheds can be characterized as living entities that change fluidly through time. Streamflow is the last check paid in the water balance – it is the residual after all other bills have been paid such as transpiration, evaporation, sublimation and all other losses. Water yield from any given watershed can be impacted by vegetation change, watershed management such as grazing, forestry practices, mining, diversions, dams and a host of related factors. In order to isolate and quantify changes in water yield due to climate change, these other factors must also be identified and quantified. Operational hydrologic models for the most part grossly simplify the complexities of watershed response due to the lack of data. For the most part they operate on some snow and precipitation data as water balance inputs, temperature as the sole energy input, gross estimations of watershed losses mostly represented by a generic rule curve and streamflow as an output to achieve a mass balance. Temperature is not the main energy driver in snowmelt, short wave solar energy is. Hydrologic models using temperature as the sole energy input can overestimate the impacts of warming.

Hydrologic Models

Operational hydrologic models on the whole are a very simplistic lot. They  represent huge complexities of watershed processes in a few lines of code by averaging or lumping inputs such as precipitation and temperatures and defining a few relatively ‘homogeneous’ areas of supposed similar characteristics. Aside from the systematically biased streamflow, snowpack, temperature and precipitation input data problems these models calibrate from and the adage applies – garbage in garbage out… or biased data in – bias continues in output, many of these models have been simplified to the point where they may not have the ability to accurately quantify climate change outside the normal range of calibration.


This figure represents the workhorse of hydrologic models, the Sacramento Model. It is a basic ‘tank’ based model where ‘tanks’ of various sizes hold water from inputs such as snowmelt and precipitation then release it to streamflow. Your basic tanks are the upper zone and lower zone with the lower zone divided into 2 separate tanks. The water level in each tank determines the total outflow to the stream. In just a few lines of code – essentially adding up the flow of each tank gives us streamflow for a give time step. Precipitation or snowmelt derived from a simple mean average basin temperature provide input to the surface tank which provides input to the lower tanks. Energy input to the snowpack portion of the model is air temperature. In an operational context, air temperature is the most widely used variable because it is normally the only data available and it is highly relational to total energy input over the normal range of model calibration. Models have been developed that have deliberately chosen the most simple input output so as to be useful in a wide range of areas such as the Snowmelt Runoff Model from Martinec and Rango.

              Snowmelt Runoff Model Structure (SRM)

Each day, the water produced from snowmelt and from rainfall is computed, superimposed on the calculated recession flow and transformed into daily discharge from the basin according to Equation (1):

Qn+1 = [cSn · an (Tn + ΔTn) Sn+ cRn Pn][(A*10000)/86400]⋅ (1-kn+1) + Qn kn+1 (1)

where: Q = average daily discharge [m3s-1]

c = runoff coefficient expressing the losses as a ratio (runoff/precipitation), with cS referring to snowmelt and cR to rain

a = degree-day factor [cm oC-1d-1] indicating the snowmelt depth resulting from 1 degree-day

T = number of degree-days [oC d]

ΔT = the adjustment by temperature lapse rate when extrapolating the temperature from the station to the average hypsometric elevation of the basin or zone [oC d]

S = ratio of the snow covered area to the total area

P = precipitation contributing to runoff [cm]. A preselected threshold temperature, TCRIT, determines whether this contribution is rainfall and immediate. If precipitation is determined by TCRIT to be new snow, it is kept on storage over the hitherto snow free area until melting conditions occur.

A = area of the basin or zone [km2]

This is the whole SRM hydrologic model – a synopsis of all the complexities of the watershed summarized in one short equation. It is a great model for its intended purpose. The energy portion of this model consists of a simple expression of a degree day factor with an adjusting factor – that is to say if the average daily temperature is above zero by some amount which is then modified by the adjustment factor, melt occurs and is processed through the model.  The greater the temperature, the more melt occurs. So how/why do these very simple models work? Because streamflow itself the result of many processes across the watershed that tend to blend and average over time and space. As long as the relationships between all processes remain relatively constant, the models do a good job. However, throw one factor into an anomalous condition, say soil moisture and model performance tends to degrade quickly.

More technical hydrologic models utilize a broader spectrum of energy inputs to the snowpack such as solar radiation. These models more accurately represent energy input to snowmelt but are not normally used in an operational context because the data inputs are not available over wide geographic areas.

The energy balance to a snowpack can be summarized as follows:

Energy Balance

M = Qm/L

Where Qm is the amount of heat available for the melt process and L is the latent heat of Fusion and M is Melt

Qs= Qis-Qrs-Qgs+Qld-Qlu+Qh+Qe+Qv+Qg-Qm

Qs is the increase in internal energy storage in the pack

Qis is the incoming solar radiation

Qrs is incoming energy loss due to reflection

Qgs is energy tranferred to soil

Qld is longwave energy to the pack

Qlu is longwave energy loss from the pack

Qh is the turbulent transfer of sensible heat from the air to the pack

Qe is the turbulent transfer of latent heat (evaporation or sublimation) to pack

Qv energy gained by vertical advective processes (rain, condensate, mass removal via evaporation/sublimation)

Qg is the supply of energy from conduction with the soil, percolation of melt and vapor transfer)

During continuous melt, a snowpack is isothermal at 0 degrees C and therefore Qs is assumed negligible as is Qgs… Therefore


where Qn is the net all wave radiation to the pack.

All of these processes in many hydrologic models are summarized in one variable – average air temperature for a given area. It is interesting to note that temperature works only on the surface of the snowpack and that a snowpack in order to melt has to be isothermal from top to bottom else melt from the surface refreezes at lower, colder pack layers. Snow is not mostly snow, it is mostly air. In cool continental areas such as Utah, snowpacks rarely exceed a 50% density which means that at its greatest density, it is still 50% air. Due to this fact, snow tends to be an outstanding insulator. You cannot pound temperature into a snowpack. Solar radiation on the other hand can penetrate and convey energy deep into the pack and it is this mechanism that conveys by far the most energy into snow. This fact can be easily observed every spring when snowpacks start to melt. Observe south facing aspects in any location from a backyard to the mountains and see from a micro to macro scale the direct influence solar radiation has with respect to temperature.

Notice in this photo patches of snow that have been solar sheltered as air temperature is very likely close to be much the same over both the melted areas and the snow covered areas in both time and space. South aspects melt first, north aspects last. Shaded areas hold snow longer than open areas.


This graph from Roger Bales expresses the energy input in watts for the Senator Beck Basin in Colorado.  The black line is the net flux to the pack or the total energy input from all sources.  The red line is the net solar input and the blue line represents all sensible energy. The difference between the red line and the black line is all energy input to the pack combined, negative and positive except net solar. From this, one can readily appreciate the relative influence each individual energy source has on snowmelt. This graph is from a dusty snow surface so the net solar is likely greater than what would be expected from a normal snowpack. However, the contrast is stark – solar radiation is the driver of snowmelt. Air temperature is a long ways back.  This of course is information that has been known for many years as illustrated in the following table from the Army Corps of Engineers in the 1960’s lysimeter experiments at Thomas Creek.

Notice that shortwave radiation is the constant day in day out energy provider, long wave, temperature,  and other sources pop up here and there.

So, what is the implication for hydrologic models that use air temperature as the primary energy input? The relationship between solar radiation and temperature will change. For a 2 degree C rise in temperature the model would see an energy input increase the equivalent to moving the calendar forward several weeks to a month – a huge energy increase. The question becomes what will the watershed actually see – will the snowpack see an equivalent magnitude energy increase?


This chart for the Weber Basin of Utah illustrates the average May temperature for various elevations and what a plus 2 degree C increase would look like. This is what the hydrologic model will see. In order to ascertain what energy increase the watershed will actually see, we go back to the graph of Bales – what the watershed will see is a more modest increase in the sensible heat line. Climate change won’t increase the hours in a day nor increase the intensity of solar radiation so the main energy driver to the snowpack, solar – will stay close to the same, all other things equal. So the total energy to the snowpack will have a modest increase but what the hydrologic model has seen is a much larger proportional increase. Thus if this factor is not accounted, the model is likely to overestimate the impacts that increased temperatures may have on snowpacks.  Hydrologic models work well within their calibrated range because temperature is closely related to solar energy. With climate change warming, this relationship may not be the stable input it once was and models may need to be adjusted accordingly.  Research needs to move in the direction of total energy input to the watershed instead of temperature based modeling. Then we can get a much clearer picture of the impacts climate change may have on water resources. Recent research by Painter et al regarding changes in snow surface albedo and accelerated runoff support the solar vs temperature energy input to the pack where surface dust can accelerate snowmelt by as much as 3 weeks or more whereas modest temperature increases would accelerate the melt by a week.

Evapotranspiration and losses to groundwater

Operational hydrologic models incorporate evapotranspiration mostly as a wild guess. I say that because there is little to no data to support the ‘rule curve’ the models use to achieve these figures. A rule curve is normally developed through the model calibration process. The general shape of the hydrograph is developed via precipitation/snow inputs and then the mass balance is achieved through the subtraction of ET data so the simulated and the observed curves fit and there is no water left over. As a side, some water may be tossed into a deeper ground water tank to make things somehow more realistic. Some pan evaporation data here and there sporadic in time and space with no transpiration data.  So how are these curves derived? Mostly from mathematical calibration fit – one models the streamflow first with precipitation/snow input, you get the desired shape of the hydrograph and then you get the final mass balance correct by increasing or decreasing the ET curve and the losses to deep groundwater. The bottom line is that these parameters have no basis in reality and are mathematically derived to achieve the correct mass balance. We have no clue what either one actually is. This may seem like a minor problem until we see what part of the hydrologic cycle they comprise.


In this chart we have a gross analysis of total watershed snowpack and annual streamflow. Higher elevation sites such as the Weber at Oakley have a much higher per acre water yield than do lower elevation watersheds such as the Sevier River at Hatch. However – in many cases there are far greater watershed losses than snowpack runoff that actually makes it past a streamgage, typical of many western watersheds where potential ET often exceeds annual precipitation. Streamflow, again, is a residual function, that water that is left over after all watershed bills are paid. We model most often the small part of the water balance and grossly estimate ET and groundwater losses. At Lake Powell, between 5 and 15% of the precipitation/snow model input shows up as flow. Small changes to the watershed loss rates or our assumptions about these loss rates can have huge implications on model results. The general assumption in a warming world is that these watershed losses will increase. Higher temperatures lead to higher evaporative losses which are the small part of the ET function – but will transpiration increase? This is a question that needs more investigation because of several issues: 1) higher CO2 can lead to more efficient plant use of water in many plants including trees and 10% to 20% less transpiration could be a significant offsetting factor in water yield and 2) watershed vegetative response to less water either through natural mechanisms (massive forest mortality such as we currently see) or mechanical means could also alter the total loss to ET. The assumptions made on the energy input side of the model together with the assumptions on watershed loss rates are likely the key drivers of model output and both have substantial problems in quantification.


Is average temperature a good metric to assess potential snow and streamflow changes?

Seeing that solar radiation is the primary energy driver to snow ablation we then make the observation that in winter the northern latitudes have very little of that commodity. Without the primary driver of snowmelt, solar radiation, snowpacks are unlikely to experience widespread melt. We then ask the question – is average temperature a good indicator of what might happen? There is at least a 50% -80% probability that any given storm on any given winter day will occur during a period of coldest daily temperature – i.e. nighttime, early morning or late evening. The further north a given point is in latitude, the higher that probability. Once snowpack is on the ground in the mountains of Utah and similar high elevation cool continental climate states, sensible heat exchange is not likely to melt it off. Thus minimum temperature or some weighted combination below average and perhaps a bit above minimum temperature might be a better metric.


In this graph two SNOTEL site minimum average monthly temperatures plus a 2 degree increase are displayed.  Little Grassy is the most southern low elevation (6100 ft) site we have. It currently has a low snowpack (6inches of SWE or less) in any given year and is melted out by April 1. Steel Creek Park is at 10,200 feet on the north slope of the Uintah Mountains in northern Utah – a typical cold site. As you can see, a 2 degree increase in temperature at Little Grassy could potentially shorten the snow accumulation/ablation seasons by a week or so on either end. This is an area which contributes to streamflow in only the highest of snowpack years and as such, a 2 week decrease in potential snow accumulation may be difficult to detect given the huge inter annual variability in SWE. A two degree rise in temperature at Steel Creek Park is meaningless – it would have little to no impact on snow accumulation or ablation. Thus most/much/some of Utah and similar areas west wide may have some temperature to ‘give’ in a climate warming scenario prior to having significant impacts to water resources.  Supporting evidence for this concept comes from the observation that estimates of temperature increases for Utah are about 2 degrees or so and we have as yet, not been able to document declines in SWE or its pattern of accumulation due to that increase. A question for further research would be – at what level of temperature increase could we anticipate temperature impacting snowpacks.

More rain, less snow

In the west where snow is referred to as white gold, the potential of less snow has huge financial implications from agriculture to recreation. The main reason many streams in the west flow at all is because infiltration capacity and deeper soil moisture is exceeded due to snowmelt of 1 to 2 inches per day over a 2 to 12 week period keeping soils saturated and excess water flowing to the stream. In the cool continental areas of the west, it can be easily demonstrated that 60%, 70%, 80% and in some cases exceeding 95% of all streamflow originates as snow. Summer precipitation has to exceed some large extent and magnitude to have any impact on streamflow at all and typically when it does, it pops up for a day and immediately returns to base flow levels. So more rain, less snow has a very ominous tone and over a long period of time, if snowpacks indeed dwindle to near nothing, very serious impacts could occur. In the short run in a counterintuitive manner, rain on snow may actually increase flows. Let’s examine how this might occur. Currently, the date snowpacks begin is hugely variable and dependent on elevation, it can range from mid September to as late as early December. If rain occurs in the fall months it is typically held by the soil through the winter months and contributes to spring runoff by soil saturation. Soils that are dry typically take more of an existing snowpack to bring them to saturation prior to generating significant runoff. Soils that are moist to saturated take far less snowmelt to reach saturation and are far more efficient in producing runoff.


In this chart of Parrish Creek along the Wasatch Front in Utah we see the relationship between soil moisture (red), snowpack (blue) and streamflow (black).  In the first 3 years of daily data, we see peak SWE was identical in all years but soil moisture was very low the first year, very high the second year and average the third year and the corresponding streamflows from identical snowpacks were low, high and average. In the fourth year snowpacks were low as was soil moisture and the resulting streamflow was abysmal.  In the fith year, snowpacks were high but soil moisture was very low and streamflow was mediocre having lost a major portion of the snowpack to bring soils to saturation. Soil moisture can have a huge impact on runoff. Thus fall precipitation on the watershed as rain can be a very beneficial event – some of course is lost to evapotranspiration but that would be the most significant loss.


In this chart of the Bear River’s soil moisture we see exactly that case – large rain events in October brought soil moisture from 30% saturation up to 65% where it remained through the winter months till spring snowmelt. This is a very positive situation that increases snowmelt runoff efficiency. Rain in the fall months is not necessarily a negative. Now lets look at rain in the spring time. This is typically rain on snow kinds of events and in fact, this from a water supply viewpoint is also very positive. If for example a watershed is melting 2 inches of SWE per day and watershed losses are 1 inch per day, then we have 1 inch of water available for runoff. Now, say we have this same scenario and we have a 1 inch rain on snow event. Then we have 2 inches of SWE melt plus 1 inch of rainfall for a total input of 3 inches and the same loss rate of 1 inch per day yields 2 inches of runoff, double the runoff for that particular day.  Twice the runoff means more water in reservoirs. Where this eventually breaks down is where the watershed aerial extent of snowpack becomes so small towards the end of melt season the total amount of water yield becomes inconsequential. If snowmelt due to temperature increases is only 1 week, then more rain less snow may not be a huge factor in water yield. When this does become a significant problem, i.e. when snow season is shortened by ‘X’ weeks should be a subject for further research. For the short term, 50 years or so, water yields in the Colorado may not likely see significant impacts from more rain/less snow and watershed responses will likely be muddled and confused by vegetation mortality. (Mountain Pine Beetle Activity May Impact Snow Accumulation And Melt. Pugh). For the short term, total precipitation during the snow accumulation/ablation season is likely a much more relevant variable than temperature. Small increases in precipitation at the higher elevations may well offset any losses in water yield from the current marginal water yield producing areas at lower elevations. A decrease in this precipitation in combination with temperature increases would be the worst scenario.

SWE to Precipitation ratios

When trying to express this concept of more rain, less snow the SWE to PCP ratio was conceived as a metric to numerically express the observed change. When developing a metric that purports to be related to some variable it is important to make sure mathematically and physically that the metric does what it was intended to do and not to have other factors unduly influence the outcome. Simply said, the SWE to PCP metric was intended to show how increased temperatures have increased rain events and decreased snow accumulation.  This metric should be primarily temperature related with only minor influences from other factors. The fact is this metric is riddled with factors other than temperature that may preclude meaningful results.  It in reality is a better indicator of drought than it is one of temperature.




In these two graphs one can see that the SWE to PCP ratio is a function of precipitation magnitude and as such is influenced by drought more than temperature. The physical and mathematical reasons are detailed in the paper ‘Characteristics of SWE to PCP Ratios in Utah’ available at the link above.


Many hydrologic models have serious limitations on both the energy input side as well as the mass balance side of watershed yield with respect to ET and ground water losses that can influence the results of temperature increases. It is possible that many systematically overestimate the impacts of temperature increases on water yields. Systematic bias in the data used by models can also predispose an outcome. What model is used in these kinds of studies matters – snowmelt models that incorporate energy balance components such as solar radiation in addition to temperature likely produce more realistic results than temperature based models. Assumptions about ET and groundwater losses can have significant impacts to results. Metrics developed to quantify specific variables or phenomena need to be rigorously checked in multiple contexts to insure they are not influenced by other factors.

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