Chapter 6 Physical Process Models

6.1 Snowmelt Models

6.1.1 Learning Module 9

6.1.1.1 Background:

Understanding snowmelt runoff is crucial for managing water resources and assessing flood risks, as it plays a significant role in the hydrologic cycle. Annual runoff and peak flow are influenced by snowmelt, rainfall, or a combination of both. In regions with a snowmelt-driven hydrologic cycle, such as the Rocky Mountains, snowpack acts as a natural reservoir, storing water during the winter months and releasing it gradually during the spring and early summer, thereby playing a vital role in maintaining water availability for various uses downstream. By examining how snowmelt interacts with other factors like precipitation, land cover, and temperature, we can better anticipate water supply fluctuations and design effective flood management strategies.

Learning objectives:

In this module, our primary focus will be modeling snowmelt as runoff, enabling us to predict when it will impact streamflow timing. We will consider some factors that may influence runoff timing. However, the term ‘snowmelt modeling’ is a field in itself and can represent a lifetime worth of work. There are many uses for snowmelt modeling (e.g., climate science and avalanche forecasting). If you are interested in exploring more on this subject, there is an excellent Snow Hydrology: Focus on Modeling series offered by CUAHSI’s Virtual University on YouTube.

Helpful terms:

The most common way to measure the water content of the snowpack is by the Snow Water Equivalent or SWE. The SWE is the water depth resulting from melting a unit column of the snowpack.

6.1.1.2 Model Approaches

Similar to the model development structure we discussed in the last module, snowmelt models are generally classified into three different types of abalation algorithms

Empirical and Data-Driven Models: These models use historical data and statistical techniques to predict runoff based on the relationship between snow characteristics (like snow area) and runoff. They use past patterns to make predictions about the future. The emergence of data-driven models has benefited from the growth of massive data and the rapid increase in computational power. These models simulate the changes in snowmelt runoff using machine learning algorithms to select appropriate parameters (e.g., daily rainfall, temperature, solar radiation, snow area, and snow water equivalent) from different data sources.

Conceptual Models: These models simplify the snowmelt process by establishing a simple, rule-based relationship between snowmelt and temperature. These models use a basic formula based on temperature to estimate how much snow will melt.

Physical Models: The physical snowmelt models calculate snowmelt based on the energy balance of snow cover. If all the heat fluxes toward the snowpack are considered positive and those away are considered negative, the sum of these fluxes is equal to the change in heat content of the snowpack for a given time period. Fluxes considered may be

  • net solar radiation (solar incoming minus albedo),
  • thermal radiation,
  • sensible heat transfer of air (e.g., when air is a different temperature than snowpack),
  • latent heat of vaporization from condensation or evaporation/sublimation, heat conducted from the ground,
  • advected heat from precipitation

examples: layered snow thermal model (SNTHERM) and physical snowpack model (SNOWPACK),

Many effective models may incorporate elements from some or all of these modeling approaches.

6.1.1.3 Spatial complexity

We may also identify models based on the model architecture or spatial complexity. The architecture can be designed based on assumptions about the physical processes that may affect the snowmelt to runoff volume and timing.

Homogenous basin modeling: You may also hear these types of models referred to as ‘black box’ models. Black-box models do not provide a detailed description of the underlying hydrological processes. Instead, they are typically expressed as empirical models that rely on statistical relationships between input and output variables. While these models can predict specific outcomes effectively, they may not be ideal for understanding the physical mechanisms that drive hydrological processes. In terms of snow cover, this is a simplistic case model where we assume:

  • the snow is consistent from top to bottom of the snow column and across the watershed
  • melt appears at the top of the snowpack
  • water immediately flows out the bottom

This type of modeling may work well if the snowpack is isothermal, if we are interested in runoff over large timesteps, or if we are modeling annual water budgets in lumped models.

Vertical layered modeling: Depending on the desired application of the model, snowmelt may be modeled in multiple layers in the snow column (air-snow surface to ground). Climate models, for example, may estimate phase changes or heat flux and consider the snowpack in 5 or more layers. Avalanche forecasters may need to consider grain evolution, density, water content, and more over hundreds of layers! Hydrologists may also choose variable layers, but many will choose single- or two-layer models for basin-wide studies, as simple models can be effective when estimating basin runoff. Here is a study by Dutra et al. (2012) that looked at the effect of the number of snow layers, liquid water representation, snow density, and snow albedo parameterizations within their tested models. Table 1 and figures 1-3 will be sufficient to understand the effects of changes to these parameters on modeled runoff and SWE. In this case, the three-layer model performed best when predicting the timing of the SWE and runoff, but density improved more by changing other parameters rather than layers (Figure 1).

Lateral spatial heterogeneity: The spatial extent of the snow cover determines the area contributing to runoff at any given time during the melt period. The more snow there is, the more water there will be when it melts. Therefore, snow cover tells us which areas will contribute water to rivers and streams as the snow melts. In areas with a lot of accumulated snow, the amount of snow covering the ground gradually decreases as the weather warms up. This melting process can take several months. How quickly the snow disappears depends on the landscape. For example, in mountainous ecosystems, factors like elevation, slope aspect, slope gradient, and forest structure affect how the snow can accumulate, evaporate or sublimate and how quickly the snow melts.

For mountain areas, similar patterns of depletion occur from year to year and can be related to the snow water equivalent (SWE) at a site, accumulated ablation, accumulated degree-days, or to runoff from the watershed using depletion curves from historical data. Here is an example of snow depletion curves developed using statistical modeling and remotely sensed data. The use of remotely sensed data can be incredibly helpful to providing estimates in remote areas with infrequent measurements. Observing depletion patterns may not be effective in ecosystems where patterns are more variable (e.g., prairies). However, stratified sampling with snow surveys, snow telemetry networks (SNOTEL) or continuous precipitation measurements can be used with techniques like cluster analyses or interpolation, to determine variables that influence SWE and estimate SWE depth or runoff over heterogeneous systems.

You can further explore all readings linked in the above section. These readings may assist in developing the workflow for your term project, though they are optional for completing this assignment. However, it is recommended that you review the figures to grasp the concepts and retain them for future reference if necessary.

6.1.1.4 Model choices: My snow is different from your snow

When determining the architecture of your snow model, your model choices will reflect the application of your model and the processes you are trying to represent. Recall that parsimony and simplicity often make for the most effective models. So, how do we know if we have a good model? Here are a few things we can check to validate our model choices:

Model Variability: A good model should produce consistent results when given the same inputs and conditions. Variability between model runs should be minimal if the watershed or environment is not changing.

Versatility: Check the model under a range of scenarios different from the conditions under which it was developed. The model should apply to similar systems or scenarios beyond the initial scope of development

Sensitivity Analysis: We reviewed this a bit in the Monte Carlo module. How do changes in model inputs impact outputs? A good model will show reasonable sensitivity changes in input parameters, with outputs responding as expected.

Validation with empirical data: Comparison with real-world data checks whether the model accurately represents the actual system

Applicability and simplicity: A good model should provide valuable insights or aid in decision-making processes relevant to the problem it addresses. It strikes a balance between complexity and simplicity, avoiding unnecessary intricacies that can lead to overfitting or computational inefficiency while sufficiently capturing the system’s complexities.

6.2 Evapotranspiration

6.2.1 Learning Module 10

20pnts

6.2.1.1 Background

Suggested reading: Forest Evapotranspiration: Measurement and Modeling at Multiple Scales

Evapotranspiration (ET) encompasses all processes through which water moves from the Earth’s surface to the atmosphere, comprising both evaporation and transpiration. This includes water vaporizing into the air from soil surfaces, the capillary fringe of groundwater, and water bodies on land. Much like snowmelt modeling, ET modeling and measurements are critical to many fields and could be a full course on its own. We will be focused on the basics of ET, modeling and data retrieval methods for water balance in hydrological modeling. Evapotranspiration is an important variable in hydrological models, as it accounts for much of the water loss in a system, outside of discharge. Transpiration, a significant component of ET, involves the movement of water from soil to atmosphere through plants. This occurs as plants absorb liquid water from the soil and release water vapor through their leaves. To gain a deeper understanding of ET, let’s review transpiration.

6.2.1.1.1 Transpiration

Plant root systems to absorb water and nutrients from the soil, which they then distribute to their stems and leaves. As part of this process, plants regulate the loss of water vapor into the atmosphere through stomatal apertures, or transpiration. However, the volume of water transpired can vary widely due to factors like weather conditions and plant traits.

Vegetation type: Plants transpire water at different rates. Some plants in arid regions have evolved mechanisms to conserve water by reducing transpiration. One mechanism involves regulating stomatal opening and closure. These plants can minimize water loss, especially during periods of high heat and low humidity. This closure of stomata can lead to diel and seasonal patterns in transpiration rates. Throughout the day, when environmental conditions are favorable for photosynthesis, stomata open to allow gas exchange, leading to increased transpiration. Conversely, during the night or under stressful conditions, stomata may close to conserve water, resulting in reduced transpiration rates.

Humidity: As the relative humidity of the air surrounding the plant rises the transpiration rate falls. It is easier for water to evaporate into dryer air than into more saturated air.

Soil type and saturation: Clay particles, being small, have a high capacity to retain water, while sand particles, being larger, readily release water. During dry periods, transpiration can contribute to the loss of moisture in the upper soil zone.When there is a shortage of moisture in the soil, plants may enter a state of senescence and reduce their rate of transpiration.

Temperature: Transpiration rates go up as the temperature goes up, especially during the growing season, when the air is warmer due to stronger sunlight and warmer air masses. Higher temperatures cause the plant cells to open stomata, allowing for the exchange of CO2 and water with the atmosphere, whereas colder temperatures cause the openings to close.

The availability and intensity of sunlight have a direct impact on transpiration rates. Likewise, the aspect of a location can influence transpiration since sunlight availability often depends on it.

Wind & air movement: Increased movement of the air around a plant will result in a higher transpiration rate. Wind will move the air around, with the result that the more saturated air close to the leaf is replaced by drier air.

6.2.1.2 Measurements

In the realm of evapotranspiration (ET) modeling and data analysis, you’ll frequently encounter the terms potential ET and actual ET. These terms are important to consider when selecting data, as they offer very different insights into water loss processes from the land surface to the atmosphere.

Potential Evapotranspiration (PET): Potential ET refers to the maximum possible rate at which water could evaporate and transpire under ideal conditions. These conditions typically assume an ample supply of water, unrestricted soil moisture availability, and sufficient energy to drive the evaporative processes. PET is often estimated based on meteorological variables such as temperature, humidity, wind speed, and solar radiation using empirical equations like the Penman-Monteith equation.

Actual Evapotranspiration (AET): Actual ET, on the other hand, represents the observed or estimated rate at which water is actually evaporating and transpiring from the land surface under existing environmental conditions. Unlike PET, AET accounts for factors such as soil moisture availability, vegetation cover, stomatal conductance, and atmospheric demand. It reflects the true water loss from the ecosystem and is often of greater interest in hydrological modeling, as it provides a more realistic depiction of water balance dynamics.

The formula for converting PET to AET is:

AET = PET * Kc

Where:

AET is the actual evapotranspiration, PET is the potential evapotranspiration, and Kc is the crop coefficient. The crop coefficient accounts for factors such as crop type, soil moisture levels, climate conditions, and management practices. It can vary throughout the growing season as well. However, note that Kc generally is used in agricultural systems, for a uniform, well-managed crop that varies by growth stage. In natural or heterogeneous systems, we may still multiply PET by a coefficient ot estimate AET, but this value represents the integrated response of multiple vegetation types and soil conditions. It is therefore better interpreted as an effective surface coefficient rather than a true crop coefficient.

6.2.1.2.1 Direct measurements:

There are several methods to measure ET directly like lysimeters and gravimetric analysis, but this data rarely available to the public. There has been a concerted effort to enhance the accessibility of Eddy Covariance data, so the dataset mentioned in the video below may expand in the years to come.

This video focuses on CO2 as an output of eddy covariance data, but among the ‘other gases’ mentioned, water vapor is included, offering means to estimate actual ET. The video also provides a resource where you might find eddy covariance data for your region of interest.

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6.2.1.2.2 Remote sensing:

Remote sensing of evapotranspiration (ET) involves the use of satellite or airborne sensors to observe and quantify the exchange of water vapor between the Earth’s surface and the atmosphere over large spatial scales. This approach offers several advantages, including the ability to monitor ET across diverse landscapes, regardless of accessibility, and to capture variations in ET over time with high temporal resolution.

Remote sensing data, coupled with energy balance models, can be used to estimate ET by quantifying the energy fluxes at the land surface. These models balance incoming solar radiation with outgoing energy fluxes, including sensible heat flux and latent heat flux (representing ET). Remote sensing-based ET estimates are often validated and calibrated using ground-based measurements, such as eddy covariance towers or lysimeters, to ensure accuracy and reliability. It can be helpful to validate these models yourself if you have a data source available in your ecoregion as a ‘sanity check’. Keep in mind that there are numerous models available, some of which may be tailored for specific ecoregions, resulting in significant variations in estimated evapotranspiration (ET) for your area among these models. If directly measured ET data is not available, you can check model output in a simple water balance. For example, inputs - outputs for your watershed (Ppt - Q - ET) should be approximately 0 (recall from our transfer function module that it is likely not exact). If the ET estimate matches precipitation, it’s likely that the selected model is overestimating ET for your region.

Some resources for finding ET modeled from remote sensing data:

ClimateEngine.org - This is a fun resource for all kinds of data. Actual evapotranspiration can be found in the TerraClimate dataset.

OpenET - you need a Google account for this one. This site is great if you need timeseries data. You can select ‘gridded data’ and draw a polygon in your area of interest. You can select the year of interest at the top of the map, and once the timeseries generates, you can view and compare the output of seven different models.