Construction of monthly time series and homogeneity tests
Digitized time series of daily maximum (Tx) and minimum (Tn) temperature and accumulated Rainfall (R), constructed by the Kenya Meteorological Department (KMD) for their observing station at Kericho (33.35E, 0.36S), are the primary meteorological data used in the analysis. The available data cover the period 1 January 1979 to 31 December 2009 for Tx and Tn and 1 January 1980 to 31 December 2009 for R. Quality control of these data, performed at the Institute of Meteorological Training and Research (IMTR), Nairobi, included: updating of missing records, verification for new records, and range and consistency checking.
The first step in the analysis was to compute monthly mean values from the daily data for each of the three variables. Monthly means were not computed for months having more than one missing daily observation, resulting in monthly time series for Tx, Tn and P that were 97.1%, 99.2%, and 99.2% complete, respectively, for the analysis period. Following this step, the monthly time series of all three variables underwent a homogeneity test to identify any break-points (jumps) in the time series which can arise from non-climate factors such as changes in station location, instrumentation and instrument exposure. Spurious break-points can substantially influence the analysis of temporal trends in time series and their removal requires making adjustments to the original time series once they have been identified [33, 34]. Ideally, the dates of any changes in, for example, station location and instrumentation, would have been recorded in order to facilitate comparisons with the dates of any identified break-points. Here, when statistically significant break-points were identified without such documentation, it was assumed they did not represent true fluctuations in climate and were removed through adjustment of the original time series.
The open source software tool RHtestV3 (written in the R programming language and available at http://cccma.seos.uvic.ca/ETCCDMI/software.shtml) was used to check for break-points in the time series analyzed. This software tool was developed at the Climate Research Division at Environment Canada and is among the set of homogeneity testing methods recognized by the World Meteorological Organization for quality control of climatic time series . Essentially, the software tests the null hypothesis that there are no changes in the mean of a time series (which may, or may not, contain a secular trend) against the alternative hypothesis that such a shift in the mean does occur at a time k. There may be more than one break-point in the time series.
Mathematically, for a time series of variable X
) the software uses a recursive regression algorithm to test the null hypothesis
against the alternative hypothesis
where t is time, N the total number of observations, μ the mean, α and β constants, and the shift at time k equal to μ2 - μ1 . The RHtestV3 software allows prescribing the confidence level for identifying break-points; here that was set to p < 0.01. Once the adjusted Tx and Tn time series were generated they were used to compute a monthly mean temperature (Tmean) as a third temperature variable where Tmean = (Tx+Tn)/2. The mean temperature was computed as the average of the daily minimum and maximum temperature specifically to enable comparison with previous studies. However readers should be aware that the calculation of the 'true' mean temperature is more complex; ideally requiring 24 hourly measurements . The quality controlled Tx Tn and Tmean monthly data for Kericho is made available (see Additional file 1) with agreement of the Kenya Meteorological Department.
Kericho temperatures and their relation the global tropics
To facilitate comparison with other climate variables, monthly departures from the long-term (1980-2009) monthly mean values of Tx, Tn, Tmean and P were computed. To emphasize relationships with El Niño (and La Niña), an 11-month moving average was then applied to one set of the resulting time series as that is the typical time scale of individual ENSO events. Time series of monthly values (i.e., no moving average applied) of all four variables were also retained for analysis with other climate variables, including monthly time series with the linear trend removed. Tropical SST data for the period 1980-2009 were obtained from the 2.5 deg. latitude/longitude resolution Extended Reconstructed Version3b monthly gridded dataset [39
]. Monthly departures from the climatological average tropical SST were calculated and averaged over 25˚S to 25˚N, with the resulting time series then used to compute temporal correlations with different variables. A similar time series was constructed using monthly surface land temperature departures from average for the global tropics obtained from the UEATEM3 dataset which is gridded at 5.0 deg. latitude/longitude resolution [40
]. When performing t-tests on correlations between climate variables, the degrees of freedom needed to be determined. This was done using the lagged autocorrelation of respective variables [41
In the above expressions ρAi and ρBi are the ith month lag autocorrelation of variables A and B, with n set to 18 months (or the number of months when the autocorrelation remained positive if less than 18 months). N
is the number of monthly values in the full time series and N
is the number of degrees of freedom used to conduct the t-test.
Highland temperature variations based on gridded temperature analyses
The gridded data in this analysis are of 0.5 degree latitude/longitude resolution, derived by spatial interpolation of ground station observations . The data set includes the variables of maximum, minimum and mean temperature, rainfall, diurnal temperature range and vapor pressure. When direct observations of these variables are not available they are derived from other, observed variables. Time series from Versions CRU05, 2.1 and interim Version 3.0 of the UEA CRU data are plotted and investigated for consistency in variability and in trend in Tx and Tn relative to observations from Kericho.