1. Introduction
Although numerical weather prediction has greatly improved over the past decades, forecasting extreme precipitation events, especially beyond two days, remains challenging (Lalaurette 2003). Early detection of extreme precipitation events can help community responders, government stakeholders, and even the media to take appropriate action to mitigate property damage and reduce casualties (Herring et al. 2017).
Over the complex terrain of British Columbia (BC), precipitation patterns and impacts across the province vary widely. To accurately place extreme precipitation events into a historical context, a long-term complete historical record is required. However, stations with reliable precipitation data are lacking outside of southern BC (Karl et al. 1993; Odon et al. 2018). This motivates the search for the best gridded climatological dataset among the latest generation of reanalyses: the Climate Forecast System Reanalysis (CFSR) from the National Centers for Environmental Prediction (NCEP), the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim), the Japanese 55-year Reanalysis (JRA-55) from the Japan Meteorological Agency (JMA), and the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), from the National Aeronautics and Space Administration (NASA). These reanalyses, if they faithfully represent precipitation, can provide long-term, spatially and temporally continuous precipitation datasets. It is, however, important to properly evaluate them before using them, so that their characteristics are known.
In Part I of this study (Odon et al. 2018, hereinafter Part I) we assessed the performance of latest generation reanalyses with respect to daily and extreme maximum and minimum 2-m temperatures over mountainous BC. In this study we assess performance with respect to daily, multiday, and extreme precipitation (hereinafter daily and extreme PCP; defined in section 2), and examine trends in both daily and extreme PCP during the study period to determine if significant statistical changes occurred over the timespan of the dataset.
An added difficulty is that verification of precipitation extremes is more challenging than that of extreme temperatures (Bhend and Whetton 2013; van Oldenborgh et al. 2013). Because of the small spatial and time scales of precipitation, in general, numerical models do not simulate precipitation as well as they do temperature (Kendon et al. 2014; Ravishankar et al. 2016) and have limited ability to faithfully represent extreme precipitation events (Zhu et al. 2014). For instance, differences in the reanalyses’ parameterizations of convection and other physical processes can impact how well extreme precipitation events are represented (Dee et al. 2011; Lindsay et al. 2014).
Previous studies have evaluated reanalysis performance with respect to precipitation and moisture fields. Flux tower observations over the Northern Hemisphere of temperature, wind speed, precipitation, downward shortwave radiation, net surface radiation, and latent and sensible heat fluxes were used to evaluate the performance of CFSR, ERA-Interim, ERA-40, and MERRA, where ERA-40 was found to have the lowest precipitation bias and ERA-Interim best captured precipitation variability (Decker et al. 2012). Hodges et al. (2011) explored how well JRA-25, ERA-Interim, MERRA, and CFSR identify extratropical cyclones over the Northern and Southern Hemispheres and found that the latest-generation reanalyses better represent cyclones, especially in the Southern Hemisphere. Berg et al. (2003) found that ERA-40 has positive biases in precipitation over land in North America, and Ruiz-Barradas and Nigam (2005) found that ERA-40 also has positive biases in evapotranspiration during the warm season over the U.S. Great Plains. Finally, Bosilovich et al. (2015) found that MERRA-2 has a more consistent global precipitation average than MERRA and has a lower global precipitation bias than JRA-55 and CFSR when compared with the Global Precipitation Climatology Project (GPCP; Adler et al. 2003).
Precipitation is examined here because of its various financial, societal, and environmental impacts such as hydroelectric power generation (Odon et al. 2017), flooding and water management (White et al. 2016; Odon et al. 2017; Sun and Miao 2018), agriculture (Rosenzweig et al. 2001; Sun and Miao 2018), tourism (Patz et al. 2005; White et al. 2016), health (Curriero et al. 2001; Patz et al. 2005), and flora and fauna (Parmesan et al. 2000).
Furthermore, several studies have noted increases in the frequency and intensity of extreme precipitation events in various parts of the world (Mann and Emanuel 2006; Krishnamurthy et al. 2009; Donat et al. 2013; Westra et al. 2013; Ravishankar et al. 2016). An increase in extreme precipitation may lead to other impacts such as an increase in winter runoff, leading to flooding and overwhelmed drainage and sewage systems capacity (White et al. 2016; Sun and Miao 2018).
In section 2, we describe the different reanalyses and weather-station observations. In sections 3 and 4, we describe our method for dividing BC into climate zones along with the various metrics used for evaluating daily and extreme reanalysis PCP. In section 5, daily and extreme PCP from the reanalyses are evaluated. In section 6, the methods for assessing statistical nonstationarity are introduced and trends of both daily and extreme PCP are examined. Results are summarized in the conclusions.
2. Data and methods
Daily accumulated precipitation from 66 weather stations from 1 January 1980 to 31 December 2010 is used in this study to evaluate CFSR, ERA-Interim, JRA-55, and MERRA-2. The 1980–2010 study period is chosen because it is the longest overlap between the four reanalyses. MERRA-2 began in 1980 (Gelaro 2015; Gelaro et al. 2017), and CFSR ended in 31 December 2010. From 1 January 2011 forward, CFSR was extended using the NCEP Climate Forecast System, version 2 (CFSv2), operational model. Differences between the model used to produce CFSR and the operational CFSv2 may affect data evaluation past the extension date (Saha et al. 2014).
A description of the different reanalyses and of the weather-station dataset is given below. A summary of the reanalyses’ atmospheric models and configurations are presented in Table 1. Precipitation from the weather stations used in this study is not assimilated by ERA-Interim (Dee et al. 2011), MERRA-2 (Bosilovich et al. 2015), or JRA-55 (Kobayashi et al. 2015) but is indirectly assimilated by CFSR (see section 2b; Wang et al. 2011). Therefore, evaluating against these observations provides a reasonably independent measure of accuracy.
Overview of the four reanalysis datasets examined in this study.
a. Weather-station data
Because of the higher spatial variability of precipitation compared to temperature, more precipitation stations are included in this study. Of the 111 geographically dispersed precipitation stations initially selected, 45 stations with more than 4% missing data were excluded. Of the remaining 66 stations, 57 are from Environment and Climate Change Canada (ECCC) and 9 are from BC Hydro (BCH; Table 2).
Description of surface weather stations (abbrev indicates the station identifier).
Figure 1 shows the locations of all 66 stations overlaid with population distribution across BC. Fifty-seven stations are located in valleys (indicated by upside-down triangles), and nine are in nonvalley locations (right-side-up triangles).
Location of ECCC (red) and BC Hydro (blue) weather stations and British Columbia population distribution (orange). Upside-down triangles indicate valley stations; upright triangles indicate nonvalley stations. Dashed lines delineate the dominant climate zones North, Northwest, Central, South Central, Maritime West, Maritime East, Southwest, and Southeast.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Location of ECCC (red) and BC Hydro (blue) weather stations and British Columbia population distribution (orange). Upside-down triangles indicate valley stations; upright triangles indicate nonvalley stations. Dashed lines delineate the dominant climate zones North, Northwest, Central, South Central, Maritime West, Maritime East, Southwest, and Southeast.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Location of ECCC (red) and BC Hydro (blue) weather stations and British Columbia population distribution (orange). Upside-down triangles indicate valley stations; upright triangles indicate nonvalley stations. Dashed lines delineate the dominant climate zones North, Northwest, Central, South Central, Maritime West, Maritime East, Southwest, and Southeast.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Long-term time series often contain variations caused by changes in the environment surrounding the gauges, instrumentation, observing procedures including the time of observation, station location, or discontinuation of the station. As a result, variations unrelated to changes in weather and climate can be introduced into the time series. Different adjustment techniques for precipitation have been developed to address impacts on climate data homogenization (e.g., Jones et al. 1985; Peterson et al. 1998; Mekis and Hogg 1999; Vincent et al. 2002).
The methods to adjust daily rainfall and snowfall for ECCC stations are described in Mekis and Vincent (2011). For each rain gauge type, corrections were implemented to account for undercatch due to wind, evaporation, and gauge-specific wetting losses. A complete description of gauges can be found in Metcalfe et al. (1997) and Devine and Mekis (2008). For snowfall, density corrections based on coincident ruler and Nipher measurements were applied to all snow ruler measurements (Mekis and Brown 2010). Detailed descriptions of trace (nonmeasurable precipitation amount)-related issues and adjustments are given in Mekis (2005) and Mekis and Vincent (2011).
Daily total precipitation was calculated by adding a station’s daily rain and snow observations together. In case of station relocation, a new identification number is often given to the new location and observations from the two stations are combined to create a longer time series. Adjustments are applied to join the two datasets, based on standardized ratios between the sites and neighboring sites or overlapping observation periods (Vincent et al. 2009).
Data homogeneity for BC Hydro stations was assessed by BC Hydro using double-mass curves (Searcy and Hardison 1960). The theory of the double-mass curve is based on the graph of the precipitation at a station against precipitation of surrounding reference stations during the same period. A break in the slope of the double-mass curve means that a change in the constant of proportionality between the station and surrounding reference stations has occurred. The data before the date that the change occurred are modified to match the historic relationship between the station and its reference stations.
Reliable data are required to detect trends in daily and extreme PCP. When dealing with trends of daily data, it is important that the dataset is nearly complete during the studied period. Furthermore, when analyzing decade-long trends, it is important that years with many missing data, if they occur, are relatively few and not clustered during a certain time interval, because this period might have had an anomalous climate (Moberg and Jones 2005; Vicente-Serrano et al. 2010). Last, the reliability of frequency of extreme precipitation events is closely related to the sample size used during the study period (Hosking et al. 1985; Hosking 1990; Porth et al. 2001; Cai and Hames 2010). Stations with more than 1% missing data are excluded from our nonstationarity analysis, leaving 29 ECCC and 6 BC Hydro stations.
b. CFSR
In 2010, NCEP introduced CFSR. Previous NCEP reanalyses have been among the most used NCEP products in history. Many known errors in the assimilation of observational data and execution of previous reanalyses were corrected in CFSR, resulting in a superior product in most respects (Saha et al. 2010).
CFSR uses NCEP’s global coupled atmosphere–ocean model. It consists of a spectral triangular atmospheric grid (Saha et al. 2006) at a horizontal resolution of T382 (0.77 ≤ R ≤ 0.91; 38 km) and a hybrid sigma-pressure system with 64 vertical levels extending from the surface to approximately 0.26 hPa. CFSR was the first NCEP global reanalysis to directly assimilate satellite radiances and to use three-dimensional variational data assimilation (3D-Var) in a gridpoint statistical interpolation (GSI) scheme rather than a spectral statistical interpolation (SSI) scheme.
Precipitation is generated by the model during the direct assimilation of temperature and humidity information from satellite radiances (Saha et al. 2010). Then, the model-generated precipitation is corrected with the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) product (Xie and Arkin 1997)—which defines 5-day mean precipitation on a 2.5° × 2.5° latitude–longitude grid over the globe by merging information derived from gauge and satellite observations—and the CPC Unified Gauge-Based Analysis of Global Daily Precipitation (CPCU) product—which interpolates quality-controlled rain gauge reports collected from the global telecommunication system (GTS) and many other national and international archives (Saha et al. 2010) on a 0.5° × 0.5° latitude–longitude grid over the globe. Last, an algorithm accounts for orographic enhancements in precipitation (Xie et al. 2007).
c. ERA-Interim
The ECMWF introduced ERA-Interim in 2011, in part to replace ERA-40 (Dee et al. 2011). The ERA-Interim configuration uses a spectral T255 horizontal resolution (~79 km), and a hybrid sigma-pressure system with 60 vertical levels with the top of the atmosphere located at 0.1 hPa.
Some of the improvements over ERA-15 and ERA-40 include a new humidity analysis; new model physics in which the prognostic equations are solved using a semi-Lagrangian scheme, a variational bias correction of satellite radiances (Dee et al. 2011); and improvements on various technical aspects of reanalysis such as data selection, quality control, bias correction, and performance monitoring, each of which can have a major impact on the quality of the reanalysis. In addition, the use of four-dimensional variational data assimilation (4D-Var) for the atmospheric analysis in ERA-Interim is a major step forward. The improved 4D-Var scheme allows the cost function to be minimized over a 12-h assimilation time interval rather than a single time, as is the case for ERA-40 and CFSR.
Precipitation is generated by the model during the variational analysis of upper-air atmospheric fields such as temperature, wind, humidity, and ozone, in combination with direct assimilation of 2-m temperature, 2-m relative humidity, and 10-m winds from land stations and upper-air temperatures, wind, and specific humidity from radiosonde data (Dee et al. 2011).
d. JRA-55
In 2011, the JMA produced JRA-55 (Ebita et al. 2009). JRA-55 extends 55 years from 1958 to 2012 and will be continued in real time as the JMA Climate Data Assimilation System (JCDAS). JRA-55 uses a spectral model integrated at a TL319 (~55 km) horizontal resolution with 60 vertical levels up to 0.1 hPa in hybrid sigma-pressure coordinates.
It employs a 4D-Var scheme that seeks the initial condition that best fits the forecast to the observations within a 6-h assimilation interval rather than a single time. The reanalysis also contains a new radiation scheme, variational bias correction for satellite radiances, and an update on dynamical and physical processes such as the prognostic equations being solved in a semi-Lagrangian form rather than Eulerian (Ebita et al. 2011; Takeuchi et al. 2013). These upgrades significantly reduce model biases versus the JMA’s previous generation reanalysis, enhance the dynamical consistency of analysis fields, and advance the handling of satellite radiances.
Precipitation is model generated during direct assimilation of upper-air temperatures and humidity information from satellite radiances and direct assimilation of surface pressure, 2-m temperature, 2-m relative humidity, and 10-m winds from land stations and upper-air temperatures, winds, and specific humidity from radiosonde data (Ebita et al. 2011).
e. MERRA-2
The new MERRA-2 was produced by NASA in 2015. The grid used for MERRA-2 is ½° latitude and 0.625° longitude (~55 km) with 72 vertical levels in hybrid sigma-pressure coordinates from the surface to 0.01 hPa.
It uses an upgraded 3D-Var scheme that is based on GSI with a 6-h update cycle. Some other improvements over NASA’s previous generation reanalysis include an updated physics model, aerosol assimilation, and corrections in precipitation for land surface and imbalances in water and energy cycles, to name a few (Rienecker et al. 2011; Gelaro 2015; Gelaro et al. 2017).
There are two kinds of precipitation fields in the MERRA-2 system. The precipitation generated by the model during the assimilation procedure (Bloom et al. 1996; Reichle et al. 2017; PRECTOT is the variable name in the data product file) and the corrected precipitation that is seen by the MERRA-2 land surface and that modulates aerosol wet deposition over land and ocean (PRECTOTCORR is the variable name in the data product file). As mentioned, for a consistent independent evaluation of all reanalyses’ performance, the former is used in this study. The precipitation is generated by the model during the direct assimilation of temperature and humidity information from satellite radiances (Bloom et al. 1996; Koster et al. 2016).
f. PRISM dataset
Precipitation is not evenly distributed over weather-station areas in complex terrain (Taesombat and Sriwongsitanon 2009). To estimate areal precipitation, it is preferable to have as many weather stations as possible. However, spatial and temporal coverage is a limiting factor (Karl et al. 1993; Odon et al. 2018), as is accuracy and reliability of precipitation records (Metcalfe et al. 1997; Serreze et al. 2005). In addition, to evaluate the agreement between observations and reanalyses it is important to realize that each grid point in a reanalysis represents an average centered on the geographical coordinates of the grid point. By contrast, an observation represents a point measurement within a reanalysis grid box, which may or may not be representative of the gridbox average. Furthermore, grid resolution and location in each reanalysis dataset are different, and the location of a station can vary from the center to the edge of the grid box. Interpolation techniques may produce inaccurate results because of the effects of topographical variation and the limited number of available rainfall stations (Taesombat and Sriwongsitanon 2009). To identify regional and terrain biases and to improve the accuracy of areal rainfall estimation, the reanalyses are bilinearly interpolated to a high-resolution Parameter–Elevation Regressions on Independent Slopes Model (PRISM; Daly et al. 1994, 1997; Daly 2002) “climatology” for grid comparison.
PRISM climatology, produced by the Pacific Climate Impact Consortium (PCIC), the Pacific Institute for Climate Solutions (PICS), and the BC government, provides access to a 30-arc-s (~800 m) gridded precipitation climatology for the 1981–2010 climate normal period for land surface areas of BC (PCIC and PRISM Climate Group 2014). PRISM has been tested and verified throughout the United States and has been applied in numerous countries across the globe, including western Canada previously for the 1961–90 period. In this study, we use the 1981–2010 climate period.
3. Climate zones
Cramer correlation matrix and eight dominant climate zone clusters in British Columbia. Crosses indicate stations where differences in precipitation distribution are statistically significant.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Cramer correlation matrix and eight dominant climate zone clusters in British Columbia. Crosses indicate stations where differences in precipitation distribution are statistically significant.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Cramer correlation matrix and eight dominant climate zone clusters in British Columbia. Crosses indicate stations where differences in precipitation distribution are statistically significant.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Cramer’s correlation is computed for each pair χ2 statistic, and PCA is conducted on the Cramer’s correlation matrix of daily PCP. The first 41 components explain 90% of the variability in the data and are retained. The number of components is larger here than in Part I of this study because of the higher variability in precipitation. For temperature, where the Pearson correlation between the stations is high (Odon et al. 2018), it is possible to capture most of their variance using a smaller number of principal components. For precipitation, where the Cramer correlation between the stations is lower (Fig. 2), more principal components are needed to capture most of their variance.
A k-means clustering analysis is then performed on the components to arrange the data into groups. From 1 to 10 clusters were tested, and an 8-cluster solution was chosen (Fig. 2). This analysis yields eight climate zones (North, Central, Northwest, Maritime West, Maritime East, Southwest, South Central, and Southeast) that roughly match to those identified in Part I.
The Maritime climate zone from Part I has been divided into Maritime East and Maritime West, and the Southeast climate zone has been divided into Southeast and South Central. These additional climate zones highlight the differences between windward and leeward regions, which see enhanced upslope precipitation and rain shadows, respectively.
4. Verification metrics
The statistical behaviors of daily and extreme PCP are compared between observed weather-station data and their corresponding location in the reanalyses and PRISM. As in Part I, four horizontal interpolation methods were trialed for reanalysis output. Also as in Part I, the methods nearest neighbor, inverse distance weighting (IDW), and bilinear and bicubic interpolation perform very similarly; IDW is used. Furthermore, IDW from land-only grid points (omitting sea grid points) was also tested for coastal stations in the Maritime West, Maritime East, Southwest, and Northwest climate zones (a grid point is classified as a land point on the basis of each reanalysis land–sea mask). Some small variations between the two IDW methods were found, but overall, the land-only IDW is similar in result to the IDW.
a. Daily PCP
We follow the Canadian meteorological convention in defining a calendar day to be from 0601 UTC of that day to 0600 UTC of the following day. For CFSR, JRA-55, and MERRA-2, precipitation accumulation intervals are summed over this window to get daily PCP (Table 1). For ERA-Interim, precipitation is accumulated in the forecast sense; that is, it is reset to zero at 0000 and 1200 UTC. The 6-h accumulated precipitation for the 6-h periods preceding 0000, 0600, 1200, and 1800 UTC is obtained in the following manner: for 0600 UTC, the 0000 UTC 6-h accumulated precipitation is used; for 1200 UTC, the 0000 UTC 6-h accumulated precipitation is subtracted from the 0000 UTC 12-h accumulated precipitation; for 1800 UTC, the 1200 UTC 6-h accumulated precipitation is used; and for 0000 UTC, the 1200 UTC 6-h precipitation is subtracted from the 1200 UTC 12-h accumulated precipitation.
A 31-day centered rolling accumulation window is used to obtain smooth monthly mean precipitation for each calendar day. These 31-day accumulated values for each calendar day are then averaged over the 31-yr evaluation period (1980–2010). This is done for each station and reanalysis data. The percentage bias (or systematic error) is then computed to estimate how accurately each reanalysis captures monthly precipitation (31-day precipitation totals).
For the same 31-day centered rolling window, days with daily PCP below 1.0 mm are classified (and hereinafter referred to) as “dry” days, and days equal to or above 1.0 mm are classified (and hereinafter referred to) as “wet” days. In climate studies, this delineation is typically made at trace amounts or 1.0 mm (Vincent and Mekis 2006; Werner and Cannon 2016). In this study, 1.0 mm was chosen because coarse-resolution models tend to overforecast the frequency and spatial extent of light precipitation events [e.g., Zhu and Luo (2015), and also shown later in this study]. On every 31-day window, systematic error is computed from the number of wet days at a station location in the reanalysis with respect to the actual number of wet days observed at a station.
Last, wet days are divided into five nonoverlapping intervals: [1.0 mm, 50th), [50th, 75th), [75th, 90th), [90th, 95th), and [95th, 100th]. The percentiles are calculated from the entire wet-day climatological distribution, centered on each calendar day, using each station’s observed data.
This allows for an evaluation of a reanalysis’ ability to correctly capture the frequency and distribution of precipitation intensities. If the reanalysis distribution is very close to that of the observation, the number of expected occurrences in each bin will be very close. This difference between the number of “very light” {[1.0 mm, 50th)}, “light” {[50th, 75th)}, “moderate” {[75th, 90th)}, “heavy” {[90th, 95th)}, and “extreme” {[95th, 100th]} precipitation events in each dataset is given by the two-sample χ2 statistic.
b. Extreme PCP
The definition of an extreme precipitation event varies widely. One possibility is to define it as an event in which precipitation over some specified period exceeds some threshold, either at a point measured by a single rain gauge or spatially averaged over some region. The choice of threshold also varies. Some studies use fixed absolute thresholds, whereas others use a fixed percentile based on the distribution specific to a given location, so that it is specific to the location climatology. In this study, we estimate the 2- and 30-yr return levels for every station for each calendar day in the 1980–2010 study period.
Furthermore, end users of precipitation forecasts, such as hydrologists, are concerned with both peak flows and total volume of flows, especially when they deviate from climatology. Correspondingly, they require accurate estimates of precipitation intensity and accumulation over a range of time scales. For the flashy reservoirs of the BC south coast, the time scales of their total volume concerns typically range from 1 to 14 days. Hydropower facilities and their associated operating procedures are designed assuming estimated minimum and maximum volumes that could be possibly expected at various time scales. Extreme precipitation accumulations, whether accumulated over 1 or 14 days, will cause extreme total flow volumes over those time scales, pushing or possibly exceeding the limits of a hydropower facility. The effects of heavy or extreme precipitation events can be compounded if components of a hydropower facility (e.g., spill gates) are out of service for planned or unplanned maintenance. Given that flow volumes are important at a range of time scales, we examine 2- and 30-yr return levels of 1-, 3-, 7-, and 14-day accumulated precipitation (2- and 30-yr return levels are also known as 2- and 30-yr recurrence intervals, or 0.5 and 
To do this, we look for the maximum 1-, 3-, 7-, and 14-day accumulated precipitation within a 31-day centered rolling window for each calendar day (Fig. 3a). This is done for each year from 1980 to 2010 inclusive, yielding 31 annual maximum values of 1-, 3-, 7-, and 14-day accumulated precipitation for each calendar day. A 31-day window was chosen so that all values within the window are from the same time of year and would have similar climatological precipitation distributions.
(a) Diagram illustrating the 31-day centered rolling window for 9 Jul, performed over the 31-yr period. (b) GEV model fitted over the 31-day, 31-yr centered window for 1-day precipitation total at Vancouver International Airport (YVR). (c) Quantile plot for the GEV fitted model for the same day, location, and variable; if the GEV is a reasonable model, the points on the quantile plot should lie close to the unit diagonal. (d) Return-level, return-period plot for the same day, location, and variable, showing the precipitation that corresponds to a given return period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
(a) Diagram illustrating the 31-day centered rolling window for 9 Jul, performed over the 31-yr period. (b) GEV model fitted over the 31-day, 31-yr centered window for 1-day precipitation total at Vancouver International Airport (YVR). (c) Quantile plot for the GEV fitted model for the same day, location, and variable; if the GEV is a reasonable model, the points on the quantile plot should lie close to the unit diagonal. (d) Return-level, return-period plot for the same day, location, and variable, showing the precipitation that corresponds to a given return period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
(a) Diagram illustrating the 31-day centered rolling window for 9 Jul, performed over the 31-yr period. (b) GEV model fitted over the 31-day, 31-yr centered window for 1-day precipitation total at Vancouver International Airport (YVR). (c) Quantile plot for the GEV fitted model for the same day, location, and variable; if the GEV is a reasonable model, the points on the quantile plot should lie close to the unit diagonal. (d) Return-level, return-period plot for the same day, location, and variable, showing the precipitation that corresponds to a given return period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
A generalized extreme value distribution (GEV) fitted by the method of L moments dresses these 31 sample values of 1-, 3-, 7-, and 14-day accumulated precipitation for each calendar day (Figs. 3b–d). A GEV is chosen because we are interested in the statistical behavior of the 31 annual maximum values of 1-, 3-, 7-, and 14-day accumulated precipitation at each calendar day. Estimates of the 2- and 30-yr return levels of annual maximum are then obtained from the fitted GEV.
The Lilliefors (Wilks 2011) test compares the largest difference, in absolute value, between the theoretical GEV cumulative distribution function (CDF) and the observed empirical cumulative distribution function (ECDF). The null hypothesis is that the observed data are drawn from the distribution being tested (i.e., the observation ECDF and GEV CDF are indistinguishable), and a sufficiently large critical difference results in the null hypothesis being rejected.
Less than 1% of the locations and calendar days for which the null hypothesis is tested for all different accumulations totals were rejected during the 1980–2010 study period, suggesting that the annual extremes in fact can be described by a GEV distribution.
The systematic error of the 2- and 30-yr return levels was then calculated to estimate how each reanalysis captures annual extremes of 1-, 3-, 7-, and 14-day accumulated precipitation. These two return levels are chosen because less than 1% of their 90% confidence intervals (CI) overlap, indicating the difference between the two return levels is statistically significant, and because the 30-yr return level is the most extreme verifiable value given the length of the data.
To calculate their 90% CIs, 100 samples of size 31 are generated from the fitted GEV distribution for each calendar day at each station, and the 2- and 30-yr return levels are estimated from each generated sample. Then, the 5th and 95h percentiles of the resulting collection of 2- and 30-yr return levels are used as the lower and upper bounds of the 90% CIs for the true 2- and 30-yr return levels.
c. Kruskal–Wallis analysis
The mean systematic error of monthly precipitation total, two-sample χ2 statistic, and 31-day-window percentage of wet days and of 2- and 30-yr return levels of 1-, 3-, 7-, and 14-day accumulated precipitation is calculated for each station from all calendar days’ systematic errors. Comparisons among these 11 mean systematic errors of each reanalysis (CFSR, ERA-Interim, JRA-55, and MERRA-2) are performed using 11 independent Kruskal–Wallis nonparametric tests. Eleven independent Kruskal–Wallis tests are used because the mean systematic errors are skewed and because of the different magnitude and variability of each type of mean systematic error. Nemenyi’s test (Hollander et al. 2013) is applied following statistical significance at the αWalker = 9.53 × 10−3 level (α0 = 0.10) in the Kruskal–Wallis results to identify significant performance differences in pairwise comparisons between the reanalyses’ mean systematic errors.
5. Results and discussion
a. Daily PCP
We first investigate reanalysis performance for daily PCP across the climate zones. Reanalysis performance in the Northwest climate zone (Fig. 4) is representative of performance across the wetter climate zones (Northwest, Maritime West, Maritime East, and Southwest; the latter three are not shown). The seasonal cycle and magnitudes of 31-day precipitation totals are fairly well captured. All four reanalyses exhibit similar seasonal cycles and differ mostly in magnitude of annual bias (Table 3). They show a positive (wet) bias all year long for the Northwest and Maritime East climate zones. In the Maritime West (the wettest climate zone in BC and in all of Canada) and Southwest zones, JRA-55, ERA-Interim, and CFSR have a negative (dry) bias throughout the year (not shown).
Observed and reanalysis running centered 31-day precipitation totals and systematic error averaged over stations in the Northwest climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Observed and reanalysis running centered 31-day precipitation totals and systematic error averaged over stations in the Northwest climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Observed and reanalysis running centered 31-day precipitation totals and systematic error averaged over stations in the Northwest climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Averaged systematic error of monthly precipitation total (M), two-sample χ2 statistic (χ2), 31-day-window percentage of wet days (W), and 30-yr return levels of 1- (1D30), 3- (3D30), 7- (7D30), and 14-day (14D30) accumulated precipitation across wetter climate zones Northwest, Maritime West, Maritime East, and Southwest; drier climate zones North, South Central, Central, and Southeast; and all climate zones in BC (all systematic errors but the two-sample χ2 statistic are in percent).
Overall, JRA-55 and ERA-Interim outperform CFSR and MERRA-2. The latter two exhibit higher bias and higher variability in bias throughout the wetter climate zones and seasons.
In contrast, in the South-Central zone, with the driest locations in all of Canada, all reanalyses have a large wet bias all year long (not shown). In the remaining drier climate zones, North, Southeast, and Central, reanalyses have a large wet bias for most of the year and the largest wet bias during spring (Fig. 5 for Central climate zone). Again, JRA-55 and ERA-Interim outperform CFSR and, to a lesser extent, MERRA-2 (Table 3). The general wet bias in most zones could be a result of the low resolution of the reanalyses that tends to spread out precipitation into drier portions of grid cells, failing to capture the locally drier climates of lower (valley) elevations, where most stations are located.
As in Fig. 4, but for the Central climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
As in Fig. 4, but for the Central climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
As in Fig. 4, but for the Central climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
The percentages of wet and dry days and the two-sample χ2 statistic are illustrated in Figs. 6a, 6b, and 6c for the Maritime West climate zone, which is representative of the wetter climate zones (Maritime West, Southwest, Northwest, and Maritime East; the latter three are not shown). The reanalyses capture the annual cycle of precipitation frequency better than they do the precipitation amounts (Figs. 5a,c; Table 3). The two-sample χ2 statistic (Fig. 6b) is used to determine how well the reanalyses capture the histogram of observed precipitation events across all bins. Lower values are better, and 0 would indicate no difference between the observation histogram and that of the reanalysis. MERRA-2 is the best because of its consistent low values of χ2 statistic across the wetter climate zones, followed closely by JRA-55 (Table 3). In looking at the precipitation percentile bins, it is seen that reanalyses overestimate the number of very light and light precipitation events (Figs. 6d,e) and underestimate the number of moderate, heavy, and extreme precipitation events for the Maritime West and Southwest zones (Figs. 6f–h). The opposite is true for the Maritime East and Northwest (not shown).
(a) Percentage of wet days, (b) two-sample χ2 statistic, and percentage of (c) dry days and (d) very light, (e) light, (f) moderate, (g) heavy, and (h) extreme precipitation events for the Maritime West climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
(a) Percentage of wet days, (b) two-sample χ2 statistic, and percentage of (c) dry days and (d) very light, (e) light, (f) moderate, (g) heavy, and (h) extreme precipitation events for the Maritime West climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
(a) Percentage of wet days, (b) two-sample χ2 statistic, and percentage of (c) dry days and (d) very light, (e) light, (f) moderate, (g) heavy, and (h) extreme precipitation events for the Maritime West climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Reanalysis performance in the North region (Fig. 7) is representative of the drier climate zones (North, South Central, Central, and Southeast; latter three not shown). All reanalyses substantially overestimate the percentage of wet days and the opposite is true for dry days (Figs. 7a,c; Table 3). MERRA-2 and JRA-55 outperform CFSR and ERA-Interim for two-sample χ2 statistic (Fig. 6b; Table 3). Reanalyses overestimate the occurrence of very light precipitation events (Figs. 7d–h); somewhat capture light, moderate, and heavy events (Figs. 7d–g); and underestimate extreme precipitation events (Fig. 7h) for the North Southeast climate zones. For Central and South Central, all precipitation-type events are well captured.
As in Fig. 6, but for the North climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
As in Fig. 6, but for the North climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
As in Fig. 6, but for the North climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Overall, across all climate zones and reanalyses, very light and light precipitation events are overestimated. This is expected because lower-resolution models tend to overforecast such events. Extreme precipitation events are underestimated. Lower-resolution models and reanalyses typically are not able to resolve extreme precipitation maxima, especially in the wettest zones—Maritime West and Southwest.
Long-term, homogenized stations in mountainous BC are mostly located in valleys (Fig. 1). To identify regional and upper-elevation biases, each reanalysis grid is bilinearly interpolated to the PRISM grid for comparison. Similar to station-to-station comparison, JRA-55 and ERA-Interim outperform CFSR and MERRA-2 (Fig. 8). All four reanalyses show a dry bias during winter along the windward and upper elevations of the islands, Coast Mountains, and Rocky Mountains (where the Maritime West, Northwest, and Southeast climate zones are located) and a wet bias along the Interior Plateau and leeward, lower-elevation regions of Vancouver Island and the lower mainland (where the Maritime East, Southwest, and Central climate zones are located). The North climate zone has the lowest systematic error across the better reanalyses. Autumn results are similar to winter results (not shown). Summer has the lowest systematic errors across the better reanalyses (JRA-55 and ERA-Interim). MERRA-2 and CFSR exhibit a wet bias across the entire province (not shown). Spring has the largest systematic errors across all four reanalyses, with wet biases in the Maritime East, Southwest, Central, and North climate zones and dry biases across the Maritime West, Northwest, and Southeast climate zones. CFSR followed by MERRA-2 shows a larger wet bias across most of the province (not shown).
(a) Winter precipitation totals of PRISM. Winter precipitation totals, bilinearly interpolated to the PRISM grid, of (b) CFSR, (c) ERA-Interim, (d) JRA-55, and (e) MERRA-2. Systematic error of (f) CFSR, (g) ERA-Interim, (h) JRA-55, and (i) MERRA-2. The dots represent weather-station location.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
(a) Winter precipitation totals of PRISM. Winter precipitation totals, bilinearly interpolated to the PRISM grid, of (b) CFSR, (c) ERA-Interim, (d) JRA-55, and (e) MERRA-2. Systematic error of (f) CFSR, (g) ERA-Interim, (h) JRA-55, and (i) MERRA-2. The dots represent weather-station location.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
(a) Winter precipitation totals of PRISM. Winter precipitation totals, bilinearly interpolated to the PRISM grid, of (b) CFSR, (c) ERA-Interim, (d) JRA-55, and (e) MERRA-2. Systematic error of (f) CFSR, (g) ERA-Interim, (h) JRA-55, and (i) MERRA-2. The dots represent weather-station location.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
An examination of the magnitudes of the biases of each metric at each station shows that reanalysis precipitation systematic error relative to weather-station observations is highly correlated with reanalysis precipitation systematic error relative to PRISM. (PRISM and all four reanalyses are bilinearly interpolated to station locations for station-to-station comparison.) PRISM was developed to create a climatological precipitation on a regularly spaced grid that addresses spatial scales and patterns of orographic precipitation (Daly et al. 1994). This is an indication that the reanalysis biases in 31-day precipitation totals (shown for JRA-55 in Fig. 9) can be largely explained by topographic and synoptic parameters, such as terrain steepness, exposure, elevation, location of barriers, and wind speed and direction, that are incorporated into PRISM. Strong correlations are also obtained for CFSR (0.78 ≤ R ≤ 0.94), ERA-Interim (0.79 ≤ R ≤ 0.93), and MERRA-2 (0.77 ≤ R ≤ 0.91; not shown).
JRA-55 mean systematic error of 31-day precipitation totals for each of the 66 stations as a function of PRISM mean systematic error. The solid lines show the linear-regression fits.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
JRA-55 mean systematic error of 31-day precipitation totals for each of the 66 stations as a function of PRISM mean systematic error. The solid lines show the linear-regression fits.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
JRA-55 mean systematic error of 31-day precipitation totals for each of the 66 stations as a function of PRISM mean systematic error. The solid lines show the linear-regression fits.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
b. Extreme PCP
The Southwest climate zone has the highest population density, and reservoir sizes in the region are small relative to the magnitude of heavy and extreme precipitation events. These two factors make it among the most sensitive to extreme precipitation events. It is also one of the wettest regions—it has one of the highest 30-yr return levels of 1-, 3-, 7-, and 14-day accumulated precipitation, second only to the Maritime West zone. Similar to the results of daily PCP for the wetter climate zones, the Southwest (Fig. 10) and Maritime West climate zones show that all reanalyses are typically too dry for extreme precipitation events and too wet for the Northwest and Maritime East climate zones.
Thirty-year return level and systematic error of 1-day precipitation total for all four reanalyses for the Southwest climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Thirty-year return level and systematic error of 1-day precipitation total for all four reanalyses for the Southwest climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Thirty-year return level and systematic error of 1-day precipitation total for all four reanalyses for the Southwest climate zone. The vertical dashed lines indicate the change in seasons, and the colored dots represent the seasonal average.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
MERRA-2 performs best in this regard, followed by ERA-Interim and JRA-55, and then CFSR. The percent magnitude of the 1-day dry biases in 30-yr return levels is similar to those accumulated over 3, 7, and 14 days (not shown; Table 3).
For the wetter climates zones, the highest values of extreme precipitation occur during storm season (October–February for southwest BC; Fig. 10). These tend to be associated with nonconvective, synoptic systems.
For the drier climate zones, the highest values of extreme precipitation occur during summer. Biases are smaller and typically associated with thunderstorm convection. In these zones, all reanalyses generally exhibit a dry bias (e.g., North; Fig. 11), with the exceptions that MERRA-2 has a wet bias during the summer peak and JRA-55 has a near-zero bias. Furthermore, all reanalyses have smaller biases when compared with the wetter climate zones (cf. Fig. 10 and Fig. 11), indicating that 30-yr return levels of 1-, 3-, 7-, and 14-day precipitation totals are fairly well captured all year long for all accumulation periods (not shown) in drier zones. This is notably different from the inability of the reanalyses to capture the annual cycle of daily precipitation in drier zones (Fig. 5). This is somewhat surprising since one might expect relatively coarse-resolution reanalyses to capture monthly accumulated precipitation more accurately than extreme convective events.
As in Fig. 10, but for the North climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
As in Fig. 10, but for the North climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
As in Fig. 10, but for the North climate zone.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
A Kruskal–Wallis analysis indicates significant differences in mean systematic error of daily and extreme PCP between the four reanalysis datasets at the αWalker = 9.53 × 10−3 level. After multiple comparisons by Nemenyi’s test, for daily PCP, ERA-Interim, JRA-55, and MERRA-2 significantly outperform CFSR. For extreme PCP, MERRA-2 and JRA-55 significantly outperform ERA-Interim and CFSR.
All of these results are summarized in Fig. 12 where mean absolute error (MAE) of the reanalyses’ daily and extreme PCP is averaged over the entire study period and all stations. The closer the value is to 0 for a given reanalysis, the better is its performance. MERRA-2 and JRA-55 are the better reanalyses, outperforming CFSR for all metrics and, to a lesser extent, ERA-Interim for daily PCP. This averaging also hides the greater variability in bias of the poorer performing reanalyses, for which it is harder to correct. For extreme PCP, the difference between MERRA-2 or JRA-55 and ERA-Interim is more noticeable, with the former two outperforming the latter. In addition, the errors of 30-yr return levels are smaller than those of 2-yr return levels. Although MERRA-2 outperforms JRA-55 in most metrics on average, the differences are not significant.
MAE of 31-day precipitation totals, χ2 statistic, wet days, and 2- and 30-yr return levels of 1-, 3-, 7-, and 14-day precipitation totals. MAE is averaged across all 66 stations. Values closer to zero at the origin of the plot are better.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
MAE of 31-day precipitation totals, χ2 statistic, wet days, and 2- and 30-yr return levels of 1-, 3-, 7-, and 14-day precipitation totals. MAE is averaged across all 66 stations. Values closer to zero at the origin of the plot are better.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
MAE of 31-day precipitation totals, χ2 statistic, wet days, and 2- and 30-yr return levels of 1-, 3-, 7-, and 14-day precipitation totals. MAE is averaged across all 66 stations. Values closer to zero at the origin of the plot are better.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
6. Stationarity
a. Daily PCP
We assess stationarity in daily and extreme PCP distributions to determine if temporal changes are significant. If there are significant temporal changes, that would mean a traditional, nonstationary distribution (based on the 1981–2010 period) would not be appropriate to represent the present-day expected precipitation distribution. First, variations through time—for each calendar day at each station—for season precipitation totals, number of wet days, very light, light, moderate, heavy, and extreme precipitation events are modeled using linear regression to identify patterns.
Seasonal precipitation total at YVR for 9 Jul (gray), 10-yr left moving average (black), decadal averages of seasonal precipitation total (1981–90, 1991–2000, and 2001–10) (blue), and 30-yr season precipitation total averaged over the study period 1981–2010 (green). The red line shows the linear-regression fit to the three decadal mean values. Individual 90% CIs (green dotted lines) and multiple (1 − αWalker) × 100% CIs (red dotted lines) are drawn; α0 = 0.10. This example indicates that a stationary distribution is appropriate for 9 Jul because the three decadal average values all fall within both CIs.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Seasonal precipitation total at YVR for 9 Jul (gray), 10-yr left moving average (black), decadal averages of seasonal precipitation total (1981–90, 1991–2000, and 2001–10) (blue), and 30-yr season precipitation total averaged over the study period 1981–2010 (green). The red line shows the linear-regression fit to the three decadal mean values. Individual 90% CIs (green dotted lines) and multiple (1 − αWalker) × 100% CIs (red dotted lines) are drawn; α0 = 0.10. This example indicates that a stationary distribution is appropriate for 9 Jul because the three decadal average values all fall within both CIs.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Seasonal precipitation total at YVR for 9 Jul (gray), 10-yr left moving average (black), decadal averages of seasonal precipitation total (1981–90, 1991–2000, and 2001–10) (blue), and 30-yr season precipitation total averaged over the study period 1981–2010 (green). The red line shows the linear-regression fit to the three decadal mean values. Individual 90% CIs (green dotted lines) and multiple (1 − αWalker) × 100% CIs (red dotted lines) are drawn; α0 = 0.10. This example indicates that a stationary distribution is appropriate for 9 Jul because the three decadal average values all fall within both CIs.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Second, CIs (Sun et al. 2018) are implemented to assess significant changes of 10-yr means from one decade to the next of season precipitation totals, number of wet days, and very light, light, moderate, heavy, and extreme precipitation events. A sufficiently large change in means from one decade to the next indicates there is a trend, and therefore nonstationarity is required to characterize daily PCP. Small changes suggest a simpler, stationary model is accurate enough to represent precipitation. This critical difference is determined by the (1 − αWalker) × 100% CI because of multiple testing, where αWalker = 4.37 × 10−6 and α0 = 0.10. Namely, variations in the mean over successive decades are large enough to be considered to be statistically significant if they fall outside the lower and upper bounds of the (1 − αWalker) × 100% CI of the resulting difference between the means of the 10-yr periods and the 30-yr period (Fig. 13). The individual 90% CI is adopted instead of the 95% CI to reduce the probability of making a type II error—that is, to reduce the probability of failing to see that there is a trend.
Figure 14a indicates a noticeable drying trend of seasonal precipitation totals across southern BC during spring and summer (late summer in the South-Central zone) and a weaker wet trend during late summer, fall, and early winter across most of BC. The weather stations are organized by climate zones with North on top, followed by Central and Northwest, with the southern regions Maritime West, Maritime East, Southwest, South Central, and Southeast at the bottom. Similarly, precipitation frequency (Fig. 14b) suggests an increase in the number of dry days during spring and summer across most of BC (particularly for the South-Central zone in summer) and a weaker increase in the frequency of wet days during autumn and winter across southern BC. None of the trends are significant at the multiple (1 − αWalker) × 100% CI. At the individual 90% CI, the trends are generally not statistically significant, with exceptions in the Northwest and Maritime West climate zone during summer.
(a) Mean linear trend of season accumulated precipitation, and (b) mean linear trend of days with precipitation. The vertical dashed lines indicate the change in seasons, and the horizontal dashed lines delineate from top to bottom the North, Central, Northwest, Maritime West, Maritime East, Southwest, South-Central, and Southeast climate zones. Units are percent change over the 30-yr period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
(a) Mean linear trend of season accumulated precipitation, and (b) mean linear trend of days with precipitation. The vertical dashed lines indicate the change in seasons, and the horizontal dashed lines delineate from top to bottom the North, Central, Northwest, Maritime West, Maritime East, Southwest, South-Central, and Southeast climate zones. Units are percent change over the 30-yr period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
(a) Mean linear trend of season accumulated precipitation, and (b) mean linear trend of days with precipitation. The vertical dashed lines indicate the change in seasons, and the horizontal dashed lines delineate from top to bottom the North, Central, Northwest, Maritime West, Maritime East, Southwest, South-Central, and Southeast climate zones. Units are percent change over the 30-yr period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Furthermore, Figs. 15a, 15b, and 15c indicate a weak increase in the number of very light, light, and moderate precipitation events across Maritime West, East, and Southwest BC during autumn (and winter for very light events) and a weak decrease in such events during spring and summer (substantially stronger for very light events in the South-Central zone). Again they are not significant—none of the trends fall outside either the multiple (1 − αWalker) × 100% CI or the individual 90% CI. Heavy (Fig. 15d) and, in particular, extreme (not shown) precipitation events do not show any clear pattern.
Mean linear trend of (a) very light, (b) light, (c) moderate, and (d) heavy precipitation events. The vertical dashed lines indicate the change in seasons and the horizontal dashed lines delineate from top to bottom the North, Central, Northwest, Maritime West, Maritime East, Southwest, South-Central, and Southeast climate zones. Units are percent change over the 30-yr period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Mean linear trend of (a) very light, (b) light, (c) moderate, and (d) heavy precipitation events. The vertical dashed lines indicate the change in seasons and the horizontal dashed lines delineate from top to bottom the North, Central, Northwest, Maritime West, Maritime East, Southwest, South-Central, and Southeast climate zones. Units are percent change over the 30-yr period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Mean linear trend of (a) very light, (b) light, (c) moderate, and (d) heavy precipitation events. The vertical dashed lines indicate the change in seasons and the horizontal dashed lines delineate from top to bottom the North, Central, Northwest, Maritime West, Maritime East, Southwest, South-Central, and Southeast climate zones. Units are percent change over the 30-yr period.
Citation: Journal of Applied Meteorology and Climatology 58, 2; 10.1175/JAMC-D-18-0188.1
Despite some clear trends, none of the changes of 10-yr means from one decade to the next are statistically significant at the multiple (1 − αWalker) × 100% CI, and only a few isolated cases are statistically significant at the individual 90% CI. During the 1981–2010 study period, a stationary 30-yr mean is accurate enough to represent mean values of season precipitation totals, number of wet days, very light, light, moderate, heavy, and extreme precipitation events.
b. Extreme PCP
For extreme PCP, the rolling 91-day centered rolling window is maintained for 1-, 3-, 7-, and 14-day precipitation totals. A GEV dresses the 31 annual maximum values for each calendar day by the method of maximum likelihood. We compare a nonstationary GEV distribution, where only the location parameter is allowed to exhibit trend, with a stationary GEV distribution with constant location, scale, and shape parameters.
7. Conclusions
Reanalysis performance for daily and extreme precipitation (PCP) is evaluated across British Columbia (BC) during the 1980–2010 study period. To compare daily PCP among CFSR, ERA-Interim, JRA-55, and MERRA-2, the systematic error of 31-day precipitation total, wet days, and two-sample χ2 statistic is calculated. To identify performance of extreme PCP, the systematic error of 2- and 30-yr return levels of 1-, 3-, 7-, and 14-day accumulated precipitation is compared.
In reanalyses, precipitation is generally better represented over areas well covered with accurate, complete, and coherent observations, which are used to correct the reanalyses. In relatively data-sparse areas such as BC (Hacker et al. 2003; Spagnol 2005), reanalysis precipitation relies mostly on the underlying model output rather than observations (Dee et al. 2011; Lindsay et al. 2014). Namely, despite model estimation of precipitation being based on temperature and humidity information derived from the assimilated observations, approximations used in the models representation of moist processes over data-sparse areas strongly affect the quality and consistency of the hydrological cycle (Dee et al. 2011).
The model-generated precipitation in CFSR traditionally has a wet bias (Saha et al. 2010). In this study, CFSR was not the best reanalysis in any of the metrics. Results suggest a wet bias across all climate zones in BC, matching previous results that indicate a wet bias over the western Pacific Ocean and in mid–high latitudes (Saha et al. 2010; Wang et al. 2011).
JRA-55 has the most consistent, and among the smallest, systematic error throughout the year and across the different climate zones in BC. Previous studies concluded that the quality of JRA-55 improved significantly when compared with that of JRA-25 (Kobayashi et al. 2015; Harada et al. 2016), especially in the Pacific Ocean north of 30°N (Harada 2018).
ERA-Interim exhibits the largest variation in performance throughout the calendar year and across the different climate zones, with lower systematic errors across the drier climate zones than the wetter climate zones, capturing the wettest months in the dry climate zones, and missing the correct amount of precipitation during storm season in the wet climate zones. However, ERA-Interim performed fairly well for daily PCP across BC. Uppala et al. (2005) explain the various difficulties encountered in ERA-40 with the assimilation of humidity information, which led to a generally poor representation of the global transport of moisture in the atmosphere. According to our results, those problems seem to have been corrected on ERA-Interim. In addition, Uppala et al. (2005) conclude that there was an improvement over previous generation reanalysis ERA-40 to ERA-Interim in precipitation over higher latitudes.
A previous MERRA study (Bosilovich et al. 2015) suggests that the sparse coverage of precipitation gauges in high latitudes may lead to significant biases. Studies have documented the difficulty of conserving atmospheric dry mass while guaranteeing that the net source of water from precipitation and surface evaporation is equal to the change in the total atmospheric water (Trenberth and Smith 2005; Bosilovich et al. 2008; Berrisford et al. 2011). These issues were reconsidered during the development of MERRA-2. In this study, MERRA-2 performed well, particularly for extreme PCP.
In summary, JRA-55 and MERRA-2 better capture precipitation distribution across BC all year and have the lowest systematic errors across the wet climate zones during storm season. This makes them the better choices for a gridded climatological dataset of daily precipitation over BC. For daily PCP, MERRA-2 and JRA-55 are the better reanalyses followed closely by ERA-Interim. For extreme PCP, MERRA-2 and JRA-55 are the better reanalyses, with the lowest systematic errors throughout the year and across different climate zones.
According to Part I and this study, ERA-Interim performs better for daily and extreme 2-m temperature than it does for daily and extreme PCP, even though the two fields should influence one another. A possible explanation is that many reanalyses do not directly assimilate 2-m-air-temperature observations, whereas ERA-Interim does. In contrast, PCP is a model-produced field, influenced indirectly by surface and upper-air temperature and humidity observations (Dee et al. 2011; Lader et al. 2016).
There is a noticeable drying trend in precipitation total during spring and summer months across southern BC and a wet trend during early autumn for northern and southwestern BC. These patterns also manifest themselves in dry- and wet-day frequencies. The strongest signal is drying in the South-Central zone in summer. These findings add more information to previous studies. Vincent and Mekis (2006) showed that the number of days with precipitation per year also has significantly increased from 1950 to 2003 across BC, and Zhang et al. (2000) showed a distinct drying pattern in the southern regions of BC during summer and spring during the second half of the twentieth century. Last, our analysis shows that spring and summer have been getting drier for much of BC, which is in line with future climate projections (Haughian et al. 2012).
The number of light and moderate precipitation events has generally increased during autumn and winter months and decreased mostly during spring and summer across BC. Despite the clear evidence of a dry trend for spring and summer months and a wet trend during autumn and winter months, the trends are not as discernible for precipitation intensity. Last, there is no discernible pattern in changes in return levels of extreme PCP or frequency of heavy and extreme precipitation events. A different study also showed no consistent trends in the number of precipitation extremes during the last century (Zhang et al. 2001). By contrast, Groisman et al. (2005) showed an increase in heavy and very heavy precipitation events south of 55°N from 1910 to 2001 across BC. The lack of consistency between periods and methods for computing the trends has made it difficult to compare results across different studies. One possibility is that changes in precipitation were occurring too slowly to be discerned in the 31-yr study period, given the considerable year-to-year variability in precipitation. Therefore, it is possible that with a longer record discernible trends may be found. For this 31-yr study period, apart from some isolated cases, no statistically significant trends are found. Thus, a stationary distribution is sufficient to represent daily and extreme PCP over BC.
Part I shows that, across mountainous BC, ERA-Interim is the most consistent and accurate reanalysis for daily and extreme temperature, with JRA-55 second. This paper shows that JRA-55 is the most consistent reanalysis for daily and extreme precipitation, followed by MERRA-2. More consistent biases are favored, because they are more easily removed by bias correction. It is important to note that, as expected, the results for daily and extreme temperatures are more conclusive than the results for daily and extreme precipitation, since models do not simulate precipitation as well as they do temperature (Kendon et al. 2014; Ravishankar et al. 2016) and have difficulties in representing extreme precipitation (Zhu et al. 2014). Because of higher variability in precipitation across BC, there is a large variation in performance—even for the better reanalyses JRA-55 and MERRA-2—across the different climate zones and seasons. Furthermore, the longer JRA-55 record is advantageous in that we expect the standard errors (of the estimated parameters used in extremes modeling and the resulting return levels) to decrease as the sample size increases (Hosking et al. 1985; Hosking 1990; Cai and Hames 2010).
From these findings, and the temperature findings in Part I, JRA-55 is recommended as the most accurate reanalysis over BC. This study concludes that for daily PCP the JRA-55 systematic error relative to weather-station observations is highly correlated with JRA-55 systematic error relative to PRISM. This result suggests that the biases can be explained by topographic and synoptic parameters—parameters that were implemented in the development of PRISM. The authors plan to implement bias corrections, on the basis of error dependencies found in Part I and this study, in JRA-55 to create an even more accurate gridded climatological dataset. This will then be used, in conjunction with a probabilistic forecast dataset, to create an extreme temperature and precipitation forecast index.
Acknowledgments
The authors thank BC Hydro, Mitacs, and the Natural Science and Engineering Research Council of Canada (NSERC) for providing funds for this research. In addition, we thank Doug McCollor and the University of British Columbia Weather Forecast Research Team for their support and the three anonymous reviewers for their comments and suggestions that greatly improved the paper.
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