Section 5 Calibration and Validation

After processing all of the data, the model was fitted using jags. The observation dataset was split into 80% for calibration, 20% for validation.

5.1 Parameter Estimates

5.1.1 Fixed Effects

Figure 5.1 and Table 5.1 present the estimated mean and 95% credible region interval (CRI) of each fixed effect parameter. The intercept term is not shown in the figure because the values are much larger than the other parameters, and would thus skew the scale.

Estimated Mean and 95% CRI of Fixed Effects

Figure 5.1: Estimated Mean and 95% CRI of Fixed Effects

Table 5.1: Estimated Mean and 95% CRI of Fixed Effects
Variable Mean Lower CRI Upper CRI
intercept 16.831668438 16.682524667 16.975449785
AreaSqKM 0.290520111 0.214532987 0.367534804
impoundArea 0.456016628 0.380017105 0.532435569
agriculture -0.180179569 -0.237304212 -0.124162093
devel_hi -0.123342802 -0.174409953 -0.070354748
forest -0.453606158 -0.521601617 -0.385848596
prcp2 0.037368478 0.035442637 0.039230802
prcp30 0.033889432 0.027601220 0.039870142
prcp2.da -0.044082207 -0.045919083 -0.042220414
prcp30.da -0.080723453 -0.086901209 -0.074180702
airTemp.da 0.025152719 0.001480242 0.047233232
airTemp.impoundArea -0.054816312 -0.077282009 -0.031984213
airTemp.agriculture -0.001544660 -0.019411269 0.015453974
airTemp.forest -0.026747107 -0.046134745 -0.006951219
airTemp.devel_hi -0.018879464 -0.033975352 -0.003815090
airTemp.prcp2 0.015308325 0.013553468 0.017116532
airTemp.prcp30 -0.058429824 -0.061922872 -0.054993205
airTemp.prcp2.da -0.007801793 -0.009506454 -0.006054510
airTemp.prcp30.da -0.011195140 -0.014792829 -0.007682154

5.1.2 HUC8 Random Effects

Figure 5.2 shows the estimated mean and 95% credible region interval (CRI) for each random effect and HUC8. Table 5.2 lists the estimated mean and 95% CRI of each parameter averaged over all HUC8s (mean value with standard deviation in parentheses).

Estimated Mean and 95% CRI of HUC Random Effects for Each HUC8

Figure 5.2: Estimated Mean and 95% CRI of HUC Random Effects for Each HUC8

Table 5.2: Mean and 95% CRI of HUC8 Random Effects Averaged Over All HUC8s (Mean Value and Std. Dev. in Parentheses)
Variable Count Mean Lower CRI Upper CRI
intercept.huc 144 -0.001 (0.467) -0.680 (0.538) 0.677 (0.512)
airTemp 144 2.009 (0.169) 1.781 (0.210) 2.236 (0.180)
temp7p 144 1.552 (0.335) 1.200 (0.371) 1.906 (0.377)

5.1.3 Catchment Random Effects

Figure 5.3 shows the distribution of the estimated mean for each random effect term over all catchments. CRIs are not shown due to the large number of individual catchments (8913). Table 5.3 lists the estimated mean and 95% CRI of each parameter averaged over all catchments (mean value with standard deviation in parentheses).

Distribution of estimated mean for each random effect over all catchments

Figure 5.3: Distribution of estimated mean for each random effect over all catchments

Table 5.3: Estimated mean and 95% CRI for each random effect averaged over all catchments (mean value with std. dev. in parentheses)
Variable Count Mean Lower CRI Upper CRI
intercept.site 2,971 -0.000 (1.254) -0.721 (1.267) 0.721 (1.281)
airTemp 2,971 0.000 (0.319) -0.283 (0.331) 0.283 (0.336)
temp7p 2,971 -0.000 (0.366) -0.500 (0.433) 0.499 (0.370)

5.1.4 Year Random Effects

Figure 5.4 and Table 5.4 present the mean and 95% CRI of the intercept term for each year. Recall that there are no random effects for years other than the intercept.

Estimated Mean and 95% CRI of Intercept Random Effect for Each Year

Figure 5.4: Estimated Mean and 95% CRI of Intercept Random Effect for Each Year

Table 5.4: Estimated Mean and 95% CRI of Intercept Random Effect for Each Year
Year Mean Lower CRI Upper CRI
1991 0.012 -0.317 0.324
1993 0.181 -0.100 0.500
1994 0.162 -0.122 0.486
1995 -0.069 -0.314 0.160
1996 -0.129 -0.352 0.088
1997 0.074 -0.119 0.280
1998 0.006 -0.214 0.222
1999 -0.032 -0.198 0.143
2000 -0.322 -0.439 -0.209
2001 0.186 0.084 0.287
2002 -0.014 -0.119 0.090
2003 -0.070 -0.174 0.031
2004 0.061 -0.039 0.161
2005 0.050 -0.056 0.154
2006 -0.178 -0.268 -0.087
2007 -0.179 -0.276 -0.085
2008 0.098 -0.001 0.194
2009 -0.126 -0.218 -0.036
2010 0.071 -0.011 0.152
2011 -0.086 -0.168 -0.011
2012 0.208 0.132 0.284
2013 0.135 0.059 0.208
2014 -0.024 -0.097 0.049
2015 -0.214 -0.291 -0.143
2016 0.162 0.088 0.235
2017 -0.152 -0.226 -0.080
2018 0.205 0.126 0.282
2019 -0.072 -0.151 0.007
2020 0.044 -0.036 0.123
2021 -0.035 -0.119 0.047
2022 0.043 -0.049 0.132

5.2 Goodness-of-Fit

Table 5.5 summarizes the model goodness-of-fit for all observations in the calibration and validation datasets.

Table 5.5: Summary statistics of model calibration and validation
Calibration Validation
# Daily Observations 705,509 80,035
# Time Series 7,814 863
# Catchments 2,971 566
# HUC8s 144 109
# Years 31 27
RMSE (degC) 1.061 1.342
Mean Residual (degC) 0.061 0.079
Median Residual (degC) 0.075 0.062
Mean Absolute Residual (degC) 0.813 1.021
Median Absolute Residual (degC) 0.649 0.805
Minimum Residual (degC) -7.570 -7.665
1st Percentile Residual (degC) -2.674 -3.225
99th Percentile Residual (degC) 2.659 3.697
Maximum Residual (degC) 9.196 7.411

Figure 5.5 presents scatterplots of predicted vs. observed daily mean temperature for the calibration and validation datasets. The black line is the 1:1 line of equality. The red line is a linear regression trend line.

Predicted versus Observed Daily Mean Temperature (degC) for Calibration and Validation Datasets

Figure 5.5: Predicted versus Observed Daily Mean Temperature (degC) for Calibration and Validation Datasets