Development and evaluation of Passive Microwave SWE retrieval equations for mountainous area Naoki Mizukami

1. Introduction With increasing researches into remote sensing application to snow hydrology, it has been shown the space-borne passive microwave data has potential capability of extracting snowpack volume - snow water equivalent (SWE) & snow depth (SD) - for global and regional scales. Remote sensing could provide spatially distributed snowpack data for any area of interest where few ground observations are made. The objective of this study is to examine the correlations between passive microwave data from Special Sensor Microwave Imager (SSM/I) and observed SWE for mountainous regions.

2. Background Passive microwave SWE retrievals have been developed empirically for global and regional scales. For global scale SD mapping, Chang et al. (1987) first applied a single form of empirical equation – SD = a x BTD with constant a where BTD is brightness temperature difference between 2 channels. Kelly et al. (2003) improved this algorithm by implementing spatially varying coefficient of a, reduced RMSE by 4.0 ~ 8.0 cm.

For regional scale, for instance, Meteorological Service of Canada (e.g. Goodison and Walker, 1995) have been involved into development/improvement of regional SWE retrievals for the prairie region in eastern Canada. For mountainous regions, however, few studies on passive microwave SWE retrievals have been conducted in detail probably because of 1) sparse snow observations for calibration/validation of the algorithm, 2) heterogeneous spatial snowpack distribution compared to satellite spatial resolution.

3. Data set  Daily Snowpack Telemetry (SNOTEL) SWE  Daily SSM/I brightness temperature (Tb) 7 channels (19, 37 and 85GHz) with dual polarizations (vertical and horizontal). The pixel size is 25 km x 25km  Period – 11 winter seasons ( through ), 6 months for each winter season (November through April).

4. Analysis Procedure 1.Used a single SSM/I pixel that encompass several SOTEL sites in the Wasatch Mountains. 2.Aggregate daily SWE time series and daily Tb time series into 10 day values. 3.Spatially aggregate 10 day SWE from multiple SNOTEL sites at the center of SSM/I pixel using inverse distance weighting 4.Perform stepwise regression (forward selection) to develop linear regression equations in monthly basis. The t-stat was used for stopping rule (max p-value = 0.05). 5.Model evaluation – RMSE and bias and linear correlation between microwave based SWE and SNOTEL SWE, and sensitivity test.

Predictors (21 candidates) Predictand = observed SWE 19H-19V19V-37H37H-37V37V-85H85H-85V 19H-37H19V-37V37H-85H37V-85V 19H-37V19V-85H37H-85V 19H-85V19V-85V 19H-85V  Single Tb: 19H, 19V, 37H, 37V, 85H, and 85V  Brightness temperature difference (TBD)  Polarization difference is considered to remove effect of snow wetness on microwave.  TBD is considered to remove effect on snowpack temperature on microwave

5. Study sites Longitude latitude Fig 1. The SSM/I pixel (orange dot) and 4 SNOTEL sites (yellow dots) within 25km from the center of the pixel used for regression analysis UT WY

6. Regression results Regression equation Nov SWE= (19V-85V)-0.25(37H-85V) Dec SWE= (19H-85V)+0.84(19H-37H)-0.73(85H-85V) Jan SWE= (19H) Feb SWE= (19H) Mar SWE= (19V-85H)-2.20(19H-85V) Apr SWE= (37H) Table 1. Resultant monthly regression equations. Maximum P-value for t- statistic for the predictors to be added was When no predictors less than 0.05 of p-value were left, stepwise regression analysis stopped.

7. Predicted versus Observed SWE Fig 2. Time series of SWE estimated by monthly regression equations and SWE based on SNOTEL observations (top panel) and residual (lower panel) SWE, cm Residual, cm Time

7. Predicted versus Observed SWE Fig 4. Scatter plot of estimated SWE from empirical equations versus SWE from SNOTEL SNOTEL SWE, cm Microwave derived SWE, cm R Nov0.81 Dec0.86 Jan0.66 Feb0.46 Mar0.63 Apr0.74 overall0.87

Standardized RMSE Month 7. Error characteristics Fig3. RMSE and bias for each month. The bias between -0.1 and 0.1 is plotted as “unbiased”. During spring, the equations tend to underestimate and RMSE. RMSE was standardized by standard deviation of predictand (SWE).

Fig 5. Frequency of R 2 from regression analysis with one winter season excluded from 11 winter seasons in total (11 R 2 in total). The regression analysis used the same forms of equation as the ones from stepwise regression (table 1) 8. Sensitivity test R2R2 Count

9. Model evaluation at different pixel Longitude latitude Fig 6. The SSM/I pixel (orange dot) and 5 SNOTEL sites (yellow dots) within 25km from the center of the pixel used for independent model evaluation. The pixel enclosed by orange circle was used for regression analysis (see Fig. 1) UT WY

9. Model evaluation at different pixel SNOTEL SWE, cm Microwave derived SWE, cm Fig 6. Scatter plot of estimated SWE from empirical equations (table 1) versus SWE from SNOTEL. Obvious underestimate during spring. Underestimate during spring R Nov0.71 Dec0.80 Jan0.61 Feb0.31 Mar0.34 Apr0.63 overall0.82

10. Summary and Future study  Multiple regression equations were developed using SNOTEL SWE data and passive microwave Tb in monthly basis.  Monthly regression equations explain of total variability of SWE overall.  There is some difficulty in estimating SWE in February –March (underestimate).  Future studies include Gridding ground-based SWE with statistical interpolation such as kriging. Test other equation types (polynomial) for regression analysis Test the empirical equations in the different mountain regions