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# Evaluating Gridded Hybrid/RTI Snowmelt Parameter Sensitivity

## Last Modified: 2023-12-13 14:20:47.481

Software Version

HEC-HMS version 4.11-beta.10 was used to create this example. You can open the example project with HEC-HMS v4.11 or a newer version.

# Introduction

The **Gridded Hybrid Snow**, or Radiation-derived Temperature Index (RTI), snowmelt method was introduced to HEC-HMS in version 4.11. Information on the **Gridded Hybrid Snow** method can be found in the HEC-HMS User's Manual and the HEC-HMS Technical Reference Manual.

The **Gridded Hybrid Snow** (or Radiation-derived Temperature Index, RTI) method is inherently a gridded method. There is no banded implementation of this snow accumulation and melt model. A terrain and discretization file were developed for you to use the **Gridded Hybrid Snow** method at a gage, or point, location.

The following parameters are required to use this method:

- Rain Threshold Air Temperature
- Snow Threshold Air Temperature
- Base Temperature
- Melt Factor
- Max Neg Melt Factor
- ATI Coefficient
- Wind Function
- Water Capacity

In this tutorial, a parameter sensitivity analysis will be performed using the Uncertainty Analysis compute option in HEC-HMS and a regression analysis in Microsoft Excel. In evaluating parameter sensitivity, we are trying to answer the following questions:

- Which parameters play the largest role in the outputs of interest?
- Which parameter should be investigated (and uncertainty reduced) in future efforts?

# Study Area

The Swamp Angel Study Plot (SASP) is located in the San Juan Mountains in southwestern Colorado, as shown in the following figure. SASP is located at an elevation of 11,060 ft (3,370 m) and is located in a meadow sheltered by the surrounding terrain and subalpine forest. The location of SASP allows for snowpack and precipitation measurements under minimal wind influence. SASP was used in the Earth System Model-Snow Model Intercomparison Project (ESM-SnowMIP). ESM SnowMIP is an international modeling effort that evaluates snow modeling schemes (Krinner et al. 2018).

For this tutorial, the study plot is treated as a point location. A simple HEC-HMS model with a single subbasin element was developed. The study plot has an area of 0.22 acres (0.0009 square kilometers).

# Finish Model Setup

**Create a Meteorologic Model**

Before performing a parameter sensitivity analysis, a meteorologic model must be created. Boundary conditions that are required to use the **Gridded** **Hybrid** **Snow **method include:

- Shortwave Radiation
- Longwave Radiation
- Precipitation
- Air Temperature
- Atmospheric Pressure
- Relative Humidity

Meteorological data used in this tutorial was obtained from the ESM SnowMIP data repository.

- Download the SwampAngel_HMS_Start project and unzip the file.
- Start HEC-HMS (version 4.11 or newer) and open the
*SwampAngel*project. - Expand the
**Basin Model**folder in the Watershed Explorer and select the*SwampAngel*basin model. Notice that the basin model contains a single subbasin named*SASP*. - Create a Meteorologic Model by selecting
**Components | Meteorologic Model Manager**. Click the**New...**button. Name the meteorologic model*WY2006*and click the**Create**button. - Close the
**Meteorologic Model Manager**window. - Expand the
**Meteorologic Model**folder in the Watershed Explorer and select the*InSitu*meteorologic model. - From the
**Component Editor**, select the following:- Unit System: U.S. Customary
- Shortwave: Specified Pyranograph
- Longwave: Specified Pyrgeograph
- Precipitation: Specified Hyetograph
- Temperature: Specified Thermograph
- Pressure: Specified Barograph
- Dew Point: Specified Humidograph
- Evapotranspiration: --None--
Replace Missing: Set To Default

The Meteorologic Model component editor should appear as in the figure below.

Within the

**Meteorologic Model Component Editor**, navigate to the**Basins**tab. Under the**Include Subbasins**header, select**Yes**from the drop-down menu to link the*SwampAngel*subbasin to the*WY2006*meteorologic model.A

**Basin Model**using the**Gridded Hybrid**snowmelt method**Meteorologic Model**. However, when using a gridded**Basin Model**and gridded**Meteorologic Model**, it is not necessary to link the**Basin Model**to the**Meteorologic Model**.- Select the
**Specified Pyranograph**from the**Watershed Explorer**. Under the**Gage**header, select*SWRadiation*from the drop-down menu. - Repeat the previous step and make the following selections:
- Specified Pyrgeograph:
*LWRadiation* - Specified Hyetograph:
*Precipitation* - Specified Thermograph:
*AirTemperature*- Lapse Method: --None--

- Specified Barograph:
*AirPressure* - Specified Humidograph:
*Humidity*

- Specified Pyrgeograph:
- Save the project.

## Create and Compute a Simulation Run

- Create a
**Compute | Create Compute | Simulation Run...**. Name the run*WY2006_RTI*and select the**Next**button. Select the*SwampAngel*basin model, the*WY2006*meteorologic model, and the*WY2006*control specifications on the following screens. Select the**Finish**button. - Select the
*WY2006_RTI*simulation from the**Compute Selection Box**in the**Toolbar.** - Click the
**Compute**button to run the simulation. - Navigate to the
**Results**tab and expand the**Simulation Runs**folder. - Select the
*WY2006_RTI*simulation and expand the*SASP*subbasin. - Hold the keyboard
**Ctrl**button and select the*Observed SWE*and*Snow Water Equivalent*output variables, as shown in the figure below. - Select the
**Plot**button from the**Toolbar**. The results should appear as in the figure below.

# Create and Compute an Uncertainty Analysis

- Create an Uncertainty Analysis by selecting
**Compute | Create Compute | Uncertainty Analysis...**. - Name the Uncertainty Analysis
*U_WY2006_RTI*as shown in the figure below. Click the**Next>**button. - Select the
*SwampAngel_RTI*basin model. Click the**Next>**button. - Select the
*WY2006*meteorologic model. Click the**Finish**button. - Navigate to the
**Compute**tab. A few folder titled*Uncertainty Analyses*was created. Expand the folder and select the*U_WY2006_RTI*analysis. - In the
**Component Editor**, select the gear icon next to the**Analysis Points**field. Click the checkbox next to the*Snow Water Equivalent*time series as shown in the figure below. - Click the
**Save**and**Close**buttons. - In the
**Component Editor**, enter the following for the**Start Date/Time**and**End Date/Time**:- Start Date: 02Oct2005
- Start Time: 0000
- End Date: 29Sep2006
- End Time: 0000

- Select a
**Time Interval**of 1 Hour from the drop-down menu. - Enter 1000 in the
**Total Samples**field. The**Total Samples**refers to the number of times the program will sample new parameter values and run a simulation. - Right click on the uncertainty analysis and select
**Add Parameter**. - Repeat the above step 7 more times to add a total of 8 parameters.
- The
**Rain Threshold Temperature**and**Snow Threshold Temperature**values will be sampled from**Specified Values**paired data. These sample values are uniformly distributed between -27 deg F and 37.4 deg F. The uniform distribution was used for this parameter sensitivity analysis because no information about parameter distributions was available. - In the Watershed Explorer, expand the
**Paired Data**and the**Parameter Value Samples**folder. Click the*RainThresholdTemp*node. In the**Component Editor**, select the**Table**or**Graph**tab to view the parameter value samples. - Repeat the above step to examine the
*SnowThresholdTemp*values. - Return to the
*U_WY2006_RTI*Uncertainty Analysis. - Select each parameter node and in the
**Component Editor**, select subbasin*SASP*in the**Element**drop-down menu. For the

**Rain Threshold Temperature**and**Snow Threshold Temperature**, select**Specified Values - Sequential Loop**from the**Method**drop-down menu. Select the appropriate paired data for each parameter. The**Parameter**tab for**Rain Threshold Temperature**is shown in the figure below.When using the

**Specified Values - Sequential Loop**paired data type, the**Uncertainty Analysis**will select pair-wise parameters from the tables. In other words, iteration 1 will use the parameter value at index 1, iteration 2 will use the parameter value at index 2, etc.When using the

**Specified Values - Random**paired data type, the**Uncertainty Analysis**will randomly sample from the parameter values in the table.The

**Specified Values - Sequential Loop**paired data type was used to ensure that the**Snow Threshold Temperature**was less than or equal to the**Rain Threshold Temperature**for every time step.- For the remaining parameters, select
**Simple Distribution**from the**Method**drop-down menu and**Uniform**from the**Distribution**drop-down menu. Enter the

**Minimum**and**Maximum**for each parameter using the values in the table below. For the uniform distribution, the**Minimum**and**Lower**values are the same and the**Maximum**and**Upper**values are the same.__Do not enter the units in HEC-HMS__; they are provided for clarity. The**Parameter**tab for**Liquid Water Capacity**is shown in the figure below.**Parameter****Distribution****Minimum****Maximum****Units**Base Temperature

Uniform

26 37 deg F Melt Factor

Uniform

0.003 0.01 in/deg F-6 hr Max Neg Melt Factor

Uniform

0.001 0.01 in/deg F-6 hr ATI Coefficient

Uniform

0.8 0.99 - Wind Function

Uniform

0.5 0.75 in/in Hg-6 hr Water Capacity

Uniform

0.1 5 % Turn off notes and warnings in the Message Log by selecting

**Tools | Program Settings...**. Navigate to the**Messages**tab. Under the**Display messages in the message log**and**Write messages to the log file**sections, uncheck the boxes next to**Notes**and**Warnings**, as shown in the figure below. Displaying and saving messages increases the run time of the Uncertainty Analysis.Compute the Uncertainty Analysis.

The simulation will take approximately 30 minutes to compute.

# Extract Sampled Parameter Values

- Navigate to the
**Results**tab. Expand the**Uncertainty Analyses**folder and select the**U_WY2006_SwampAngel**uncertainty analysis. The**Results**tab should resemble the figure below. - HEC-HMS provides the sampled parameter values for each realization. In addition, the SWE time series and maximum SWE value for each realization are provided. Select a
**Parameter**node to view the sampled parameter values, as in the figure below. - Open each
**Parameter**node and copy the sampled parameter values to an Excel spreadsheet. Include a data label for each parameter (e.g. "Liquid Water Capacity"). - Expand the
**SASP**subbasin node and select the**Maximum SWE**time series node. Copy the output to Excel. Include a data label for the maximum SWE output.

# Perform a Multiple Linear Regression Analysis in Excel

The parameter values are generated through random sampling. Your parameter values will be different from the values shown in this section unless the same **Seed Value** is used in the HEC-HMS Uncertainty Analysis. The **Seed Value** is used to initialize the random number generator. In general, it is __not__ advisable to change the **Seed Value** unless you are trying to duplicate results.

- Compute the mean and standard deviation of each parameter and the maximum SWE using Excel functions
**AVERAGE**and**STDEV.S**. The Excel spreadsheet should look similar to the figure below. - Before performing a regression analysis, the sampled parameters and maximum SWE output must be standardized. The 8 parameters have different units and scales. Standardization is needed so that parameters with larger standard deviations do not have greater influence on the regression results. In addition, standardization ensures that the regression coefficients have uniform units. The parameters and output were standardized by subtracting the mean and dividing by the standard deviation:

Z_i = \frac{X_i - \bar{X}}{\hat{\sigma}} - The mean and standard deviation for each standardized variable should be 0 and 1, respectively. The results of the standardization should look similar to the figure below.
- Multiple linear regression can be performed in Excel using the Analysis ToolPak. Select
**File**|**Options**. Navigate to the**Add-ins**tab on the left side of the**Excel Options**dialog box. On the bottom of the dialog box, select Excel Add-ins from the**Manage**drop-down menu and click the**Go...**button. Select the check box next to the Analysis Toolpack add-in, as in the figure below. Click the**OK**button to close the dialog box. - Navigate to the
**Data**tab |**Analysis**section |**Data Analysis**option. - Select
**Regression**in the**Data Analysis**dialog box. Click the**OK**button. - In the
**Regression**dialog box, make the following selections:- The
**Input****Y Range**is the range of cells containing the maximum SWE data (including the data label). - The
**Input****X Range**is the range of cells containing the standardized sampled parameters (including the data labels). - Check the
**Labels**box to indicate that data labels were included in the Y and X ranges. - Under the
**Output Options**, enter Results in the field next to**New Worksheet Ply**to save the regression analysis results in a new tab named*Results*.

- The
- The Regression dialog box should resemble the figure below. Click the
**OK**button perform the regression analysis.

# Analyze Results

Navigate to the **Results **tab in Excel. The bottom table (boxed in red in the figure below) shows the results of the regression analysis. The **coefficients** are used to develop a linear regression of the general form:

y = ax + b

where a is the regression coefficient and b is the intercept. In this tutorial, 8 parameters were evaluated. Therefore, the linear regression takes the following form:

y = a_1x_1 + a_2x_2 + a_3x_3 + a_4x_4 + a_5x_5 + a_6x_6 + a_7x_7 + a_8x_8 + b

A negative regression **coefficient **means that smaller parameter values increase the maximum SWE and a positive regression **coefficient **means that larger parameter values increase the maximum SWE. The **P-value** indicates whether the dependent variable is statistically significant. Low **P-values** and high **coefficient **values indicate that the parameter has a significant impact on the dependent variable, or model output.

- Select the 8 parameter labels and the corresponding regression coefficients.
Navigate to the

**Insert**tab and select**Recommended Charts**in the**Charts**section. Select the**Clustered Bar**option. Click the**OK**button. The plot should look similar to the figure below.The results of this parameter sensitivity analysis are specific to the Swamp Angel Study Plot. The regression coefficients for

**Gridded Hybrid**snowmelt parameters will vary by location. A site-specific parameter sensitivity analysis should be performed for your modeling domain.From the tornado chart above, it is easy to tell that the parameters with the greatest impact on the maximum SWE output are the

**Melt Factor**and the**Base Temperature**. The**Base Temperature**has the largest positive regression coefficient. The**Base Temperature**is the temperature above which snow melts. A high**Base Temperature**increases the temperature range at which snow remains solid, increasing the maximum SWE. The**Melt Factor**has a negative regression coefficient. A large**Melt Factor**causes the snow to melt quickly, which reduces the depth of accumulated snow and the maximum SWE.- Another way to evaluate model results is to compare individual model parameters to maximum SWE. Two parameters were selected for further analysis:
**Wind Function**and**Base Temperature**. The first plot is a comparison between the standardized**Wind Function**and standardized**Maximum SWE**. The second plot is a comparison between the standardized**Base Temperature**and standardized**Maximum****SWE**. The figures show that**Base Temperature**has a large impact on maximum SWE while**Wind Function**

The results of the regression analysis can inform calibration efforts. In calibrating the Swamp Angel model, the focus should be on parameters related to the melt rate, such as**Melt Factor**and**,**Base Temperature,**Max Negative Melt Factor.**The Excel spreadsheet used to perform the regression analysis is included below.