On-line Resource 1

Title:Projected 21st century trends in hydroclimatology of the Tahoe basin

Journal:Climatic Change

Authors:Robert Coats1, Mariza Costa-Cabral, John Riverson, John Reuter, Goloka Sahoo, Geoffrey Schladowand Brent Wolfe

(1) University of California Tahoe Environmental Researh Center, Davis, CA ()

Precipitation Bias Correction Method

Any precipitation event in each of the 12 months was subject to removal with equal likelihood, regardless of event length or precipitation total, a process we termed “resampling”. Resampling continued until the number of event days in the grid cell for each of the 12 months matched the observations at the closest meteorological station. Prior to resampling, the simulated distribution of event lengths approximately matched observations. Our resampling technique, by construct, preserved the distribution of simulated event lengths.

For the simulated future time series, resampling was carried out under the assumption that each GCM produces for each grid cell, for any given month, a consistent percentage of excess number of precipitation days, regardless of a climate warming trend. Thus, for that grid cell the same percentage of precipitation days was removed for the 100 months of September (e.g.) in a century-long future simulated time series, as the percentage removed for the 50 months of September in the historical time period for the same model. (September was cited as an example. The same applies to all 12 months.)

As an example of the quantile mapping method, Figure 1 shows the distributions of daily precipitation in all months of December within the historical period 1950-1999 for a grid cell centered southwest of the Lake. December has the highest precipitation totals of all months. The observed time series is represented in black, the GFDL simulations (previously downscaled using the constructed analogues method) are represented in red, and the PCM simulations (similarly downscaled) are represented in green. Simulations by the two GCMs have similar distributions as a result of having previously been subjected to downscaling by constructed analogues. The resulting simulated distributions under-estimate the observations, i.e., the mean precipitation intensity in wet days is lower than observations. The same was found for all of the wet-season months (November-April). Quantile mapping (see e.g. Wood et al., 2004) was used to obtain distributions of precipitation intensity in agreement with historical observations at the stations’ locations.As a result of quantile mapping, the empirical cumulative distribution function (eCDF) of simulated daily precipitation in the historical period matches the station’s observed distribution (by construct). We found that mapping at the daily time scale also resulted in monthly eCDFs in approximate agreement with observations for the winter months (i.e., the main precipitation months), and in annual distributions that are in good agreement with observations. Figure 2 shows a comparison of eCFD distributions of annual precipitation totals. After quantile mapping at the daily time scale, the resulting eCDFs (termed “final” in the figure legends and plotted in blue) match the observed eCDF (in black) more closely than the simulated eCDFs (downscaled by constructed analogues) that entered this project (in red), for both GFDL (top panel) and PCM (bottom panel).

For the future (projected) time series of precipitation, a similar technique was used. Each simulated value y is replaced by an observed value x’ having the same plotting position as a value x=y in the historical simulations. If the exact value x=y was not found in the historical simulations, then interpolation between the two nearest points was used. In the case of an extremely high value y that is larger than any value in the simulated historical time series, then a fitted theoretical distribution was used that extends the range of that historical distribution for that month. We experimented with several theoretical distributions and chose the Exponential distribution because it provides one of the best fits and is computationally simple.

Wind Bias Correction Methods

The downscaled wind speed (m sec-1) for the GFDL A2 and B1 scenarios were compared with measured records at the South Lake Tahoe Airport (SLTA) meteorological station for the period 1989 to 1998. We found that the average and standard deviation of downscaled speedsof the GFDL A2 and B1 winds were both greater than those of measured records at SLTA, though there was very little difference in mean and standard deviation between the two scenarios (Table 1). As with the precipitation data, we used quantile mapping (Wood et al., 2002) to correct the bias in the downscaled wind speed (m/s) values.

For both scenarios, the best fit between observed and modeled wind speed distributions was obtained with 6th order polynomial for modeled wind speeds < 11.0 m sec-1, and a linear equation for speeds >11.0 m sec-1, since a break in slope occurred at that speed. The R2 values for A2 were 0.9995 (< 11.0 m sec-1) and 0.946 (> 11.0 m sec-1), and for B1, 0.9996 (< 11.0 m sec-1) and 0.9979 (> 11.0 m sec-1). Figure 3shows the relationship between the rank-ordered measured and modeled wind speed, along with the best fit line for the adjustment equation. The adjusted historic data are shown in Figure 4. The curves for the B1 scenario (not shown) are similar.

Bias Correction Method for Streamflow Statistics

To remove bias in the LSPC/GFDL flow duration curves for daily discharge, we first calculated flow duration curves from both the U.S. Geological Survey record (USGS, 2009) for measured discharge (Sta. No. 10336610), and from the GFDL/LSPC modeled output for the same historic period (1972-1999). We then interpolated log discharge at equal values of exceedence (e.g. 0.1, 0.2…100 percent of the time), and found the equation (a 3rd-order polynomial, R2 = 0.995) that mapped the historic modeled curve onto the curve from the gage data. We then used this equation to adjust the projected future flow duration curves. Figure 5 shows the flow duration curves for the gage record and unadjusted GFDL/LSPC output for the same period.

The comparison of the two flood frequency curves for the Upper Truckee River USGS gage record and the GFDL/LSPC modeled flood data (1972-2008) showed that the LSPC/GFDL curve was somewhat higher than the curve from the gage data. To adjust the modeled output to the same scale as the measured discharge, we used a linear regression of the log flood magnitude from the USGS data vs. the modeled log flood magnitude for the same period, at equal recurrence intervals (R2= 0.997). The resulting equation, shown on Figure 6 was used to adjust the modeled flood frequency curves downward. We then calculated confidence limits for the estimated flood frequencies according the Bull. 17B method, and compared the calculated flood frequencies from the USGS gage record (1972-2008) with the projected frequencies for the three 33-yr periods.

The USGS curve is based on the annual maximum instantaneous flow, whereas the modeled curve is based on the annual maximum hourly flow. The latter should be slightly lower than the former, although for a basin the size of the UTR, the two values would not be much different.

Fig 1 Distributions of daily precipitation in all months of December within the historical period 1950-1999 for grid cell #4, southwest of Lake Tahoe.

Fig 2 Comparison of eCFD distributions of annual precipitation totals

Figure 3. Non-linear relation between rank-ordered GFDLA2 wind speed and rank-ordered observed records. Solid lines represent 6th order polynomial trend line for wind speed less than 11 m/s and a power regression trend line for wind speed > 11 m/s.

Figure 4. Uncorrected and bias-corrected GFDLA2 wind speed and observed records at SLTA

Figure 5 Flow duration curves for the UTR gage record, 1972-1999 and the modeled runoff from the GFDL/LSPC for the same period

Fig 6 Calculated flood frequency curves for the UTR gage record (1972-2008) and the modeled GFDL/LSPC data

Table 1. Statistics of the measured, downscaled and corrected downscaled GFDL A2 and GFDL B1 wind speed (m s-1) using data for the period 1989 to 1998.

Measured / GFDL A2 & B1
Modeled / GFDL A2 & B1
Corrected
Mean (m/s) / 2.8 / 3.3 / 2.8
SD (m/s) / 1.5 / 2.1 / 1.5