﻿ Numerical Modeling Workflow - Finite Difference Grids > View Results > Charts

# Charts

In Visual MODFLOW Flex, upon completing a successful model run, you can view several different types of charts to review your results and to facilitate model calibration:

View Charts Workflow Step

Stand-Alone Charts

See the controls section below on how to create and modify the Charts associated with the View Charts workflow step, and the individual sections listed above for further details on the stand-alone charts.

## Calibration (Calculated vs. Observed) Charts

The Calculated vs. Observed Chart consists of a scatter plot representing the comparison between the calculated and observed values at select points in time (as show below).  Simulated Heads or Concentrations can be compared to observed values and displayed on the Calculated vs. Observed Chart. For transient simulations containing many different observation times for each observation point, the quality of the model calibration will likely change throughout the simulation. Therefore, it is important to be able to evaluate the calibration at different times throughout the simulation.

 Workflow Step Flow Model (Heads) Transport Model (Concentrations)

Unfortunately, the output times generated by MODFLOW rarely coincide with the actual times when the observed data was collected or recorded in the field. However, it is generally considered a good practice to interpolate the model calculated data to the observation times in order to compare the calculated vs. observed values.  Visual MODFLOW Flex calculates the interpolated values for you; however, it is important to compare the model output times to the observations to assess the suitability of the interpolation relative to the time gap between output times and observations as well as relative to relevant stress periods and resulting changes in heads or concentrations.

The Scatter Graph of Calculated vs. Observed Values is the default Calibration Graph. This graph represents a snap-shot in time of the comparison between the values calculated by the model (Y-axis), and the values observed or measured in the field (X-axis). The situation where all data points intersect the 45 degree line on the graph where X=Y represents an ideal calibration scenario, but it is not likely to happen when developing models of real-world sites.

If the data points appear above the X=Y line, then the calculated values are larger than the observed values, and the Calibration Residual is positive, indicating that the model is over-predicting. If the data points are under the X=Y line, then the calculated values are less than the observed values, and the Calibration Residuals are negative, indicating that the model is under-predicting.  The chart above indicates the model is over-predicting head values.

## Time Series Plots

A Time-Series graph plots the value of one or more selected variable over time. In groundwater flow and contaminant transport modeling, time-series graphs are used to evaluate and compare temporal trends in the calculated Head, Drawdown, or Concentrations at selected Observation Points.

## Chart Controls

Controls to adjust the charts are shown to the left of the chart.

Mass Balance: Select this button to open the Mass Balance Charts.

Zone Budget: Select this button to open the ZoneBudget Charts.

Parameter: Select either Flow or Transport to display results from your flow or transport model, respectively.

Chart Type: Select from either Calc. vs. Obs. or Time Series.

Time: Select listed times from the dropdown to display results at the specified output time step (calculated vs. observed only)

Labels: Select the check box to show/hide labels for the plotted data points.

Observations Controls

oAll Times: Select the check box to show all times or to only use the time specified in the Time dropdown list

oAll Obs: Select the check box to show all observations

oSpecies Selection Box: Only observations for the selected species will be shown (only shown when the Parameter option is Transport)

oObservation Group Box: Only observations for the selected observation group will be shown

oLayer Selection Box: Only observations for the selected layers will be shown

oObservation Location Box: Only observations for the selected locations will be shown

Apply: updates the chart using the selections in the Observations Controls.

## Statistics

The Calibration Statistics are reported in the footer of the Calibration Plots window when the Calculated vs. Observed Scatter Graph is displayed. These statistics are calculated using the assumption that the calibration residuals are normally distributed.  The individual statistics are described below:

### Calibration Residual

The Calibration Residual (Ri) is defined as the difference between the calculated results (Xcal) and the observed results (Xobs) at selected data points (as shown in the following equation):

The absolute value maximum and minimum residuals at the selected observation points are also reported.

### Residual Mean

The Residual Mean is a measure of the average Residual value defined by the equation:

where:

n = the number of observations

Please Note: there may be cases where over-calculated and under-calculated values will negate each other, and produce a Residual Mean value close to zero. This can lead to false interpretation of the model calibration. The Residual Mean should never be used by itself as a measure of the fit between the simulated results and the observed data.

### Absolute Residual Mean

The Absolute Residual Mean is similar to the Residual Mean except that it is a measure of the average absolute Residual value defined by the equation:

The Absolute Residual Mean measures the average magnitude of the Residuals, and therefore provides a better indication of calibration than the Residual Mean.

### Standard Error of the Estimate

The Standard Error of the Estimate (SEE) is a measure of the variability of the residual around the expected residual value, and is expressed by the following equation:

### Root Mean Squared

The Root Mean Squared error (RMS) is defined by the following equation:

### Normalized Root Mean Squared

The Normalized Root Mean Squared is the RMS divided by the maximum difference in the observed head values, and is expressed by the following equation:

The Normalized RMS is expressed as a percentage, and is a more representative measure of the fit than the standard RMS, as it accounts for the scale of the potential range of data values.

For example, an RMS value of 1.5 will indicate a poor calibration for a model with a range of observed values between 10 and 20, but it will indicate an excellent calibration for a model with a range of observed values between 100 and 200. However, the Normalized RMS value for the first model would be 15%, while the Normalized RMS for the second model would be 1.5%. In the second situation, the Normalized RMS values clearly indicates the second model provides a good fit between the calculated and observed values.

### Correlation Coefficient

The Correlation Coefficient (Cor) is calculated as the covariance (Cov) between the calculated results (Xcal) and the observed results (Xobs) at selected data points divided by the product of their standard deviations. The correlation coefficient is calculated using the following equation:

The covariance is calculated using the following equation:

Where and are the mean values of calculated and observed results, respectively.

The standard deviations are calculated by the equations:

Correlation Coefficients range in value from -1.0 to 1.0. The Correlation Coefficient determines whether two ranges of data move together - i.e. whether large values of one data set are associated with large values of the other data set (positive correlation), whether small values of one data set are associated with large values of the other data set (negative correlation), or whether values in both sets are unrelated (correlation near zero).

## Export

Chart data can be exported to .CSV file, for further analysis (with Excel or other charting programs)

Just select the Export button from the toolbar when you are viewing either Calc. vs. Observed, or Time Series charts, for either Flow or Transport runs.  All calibration data will be exported to the .CSV file (not just the selections you have defined in the Chart toolbox).