The Ph.D. dissertation entitled ‘Hydrologic Response to Climate Change in California: Observational and Modeling Studies‘ by Bruce Daniels at UC Santa Cruz was a study of hydroclimatology (how climate change impacts water resources).
For this study, climate change information came not from climate models, but instead from measurements of at least 85 years of daily observations gathered from 50 California locations. These records were used to calculate the long-term trends of three precipitation timing patterns. The state-wide trends found are that rain/snow events have been lasting longer, getting weaker, and the time between them has increased.
The study then assumed that these three observed trends might continue for another 30 years. They were applied as future climate change for input to two water basins in California. The hydrology model for one basin in the snowy Sierras benefited from this future climate with 1/2 percent more streamflow. A basin on the central coast suffered 2.5 percent less recharge for water supply.
Note that these impacts were derived from just the changes of the three precipitation timing patterns. No change in the total precipitation or temperature was included.
For more details of this study please get the complete Dissertation Document.
Another key aspect of this study was statistical analysis for the proper derivation of trend values and their statistical significance when there is missing data. In the precipitation observation data there was up to 7% of the daily values missing from the records.
First was a demonstration that such missing data actually matters. This was shown by artificially injecting missing data into the long (138 years) and largely present (0.2%) Sacramento dataset. This injection caused the resulting trend values to be considerably different from their original true values.
The AutoRegressive Integrated Moving Average (ARIMA) time-series processing techniques were tried and were not useful for filling in the missing precipitation data. It seems that precipitation is just too erratic, since it can rain like crazy one day and then nothing the next. This is particularly true here in California where the interannual coefficient of variation is 30-60%, instead of the 10-30% for the rest of the country. The auto-correlation values for daily precipitation here are quite poor.
Simple exogenous imputation, where one attempts to use a nearby station’s data to fill in for missing values, was also tried and was not successful. For example, a cross-plot of precipitation for Santa Cruz versus Watsonville (just 20km away) shows practically no correlation.
What did work was a multiple imputation technique which produces a probability distribution for the missing data. The shape parameter for a suitable Weibull distribution was found through a fit to the plots of my three metrics of event Intensity, event Duration, and lull Pauses. Estimates for the missing data from each month and year were produced by taking averages from 0, 1, and 2 months before and after the date of interest along with 0, … 11 years before and after that date. From these estimates was derived a scale parameter for the Weibull distribution to use for the missing data.
This is all described in Chapter 1 of my dissertation. Then Chapter 2 details the use a permutation and Monte Carlo technique to derive statistical confidence p-values for those trend values produced in Chapter 1.