diff --git a/README.md b/README.md index e1faa7e..aa78ce8 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,12 @@ PaleoCalAdjust =================== -The programs here implement an approach for adjusting for the "paleo calendar effect" -- the impact that the changes in the length of months or seasons over time (related to the changes in the eccentricity of Earth's orbit and to precession), have on the summarization of paleoclimatic model output. The key program is `cal_adjust_PMIP3.f90` (in the folder `/f90`), which applies the adjustment to CMIP5/PMIP3-formatted files, and a related program, `month_length.f90`, that can be used to produce tables of the changing length of months over time. Figures illustrating the paleo calendar effect are in the folder `/figures`, and relevant data sets for exercising the programs are in the folder `/data`. The program `cal_adjust_PMIP3.f90` will be modified to accommodate CMIP6/PMIP4-formatted files when they become available. +This is the repository that accompanies the paper: + +Bartlein, P. J. and Shafer, S. L.: Paleo calendar-effect adjustments in time-slice and transient climate-model simulations (PaleoCalAdjust v1.0): impact and strategies for data analysis, *Geosci. Model Dev. Discuss.*, 2018, 1-36, [https://doi.org/10.5194/gmd-2018-283](https://doi.org/10.5194/gmd-2018-283), 2018. + + +The programs implement an approach for adjusting for the "paleo calendar effect" -- the impact that the changes in the length of months or seasons over time (related to the changes in the eccentricity of Earth's orbit and to precession), have on the summarization of paleoclimatic model output. The key program is `cal_adjust_PMIP3.f90` (in the folder `/f90`), which applies the adjustment to CMIP5/PMIP3-formatted files, and a related program, `month_length.f90`, that can be used to produce tables of the changing length of months over time. Figures illustrating the paleo calendar effect are in the folder `/figures`, and relevant data sets for exercising the programs are in the folder `/data`. The program `cal_adjust_PMIP3.f90` will be modified to accommodate CMIP6/PMIP4-formatted files when they become available. + + diff --git a/data/figure_data/README.md b/data/figure_data/README.md index 2b307cb..b0f3478 100644 --- a/data/figure_data/README.md +++ b/data/figure_data/README.md @@ -2,10 +2,10 @@ Data for the figures can be found in the folders here or via links as follows: -- Figs. 1, 2, 3, S2, S3, S5, S6, S7 (month-length plots): in the folder `/month_length_plots`; -- Figs. 4, 5, 6 (calendar-effect maps): links to the calendar-effects netCDF files are in the `/data/nc_files` folder; The variables plotted are `xm_harmonic_ltmdiff` (Figs. 4 and 6), `mtco_ltmdiff` and `mtwa_ltmdiff` (Fig. 5); -- Fig. 7 (TraCE plots); in the folder `/TraCE_plots`; -- Fig. S1 (orbital-parameter plots): in the folder `/orb_param_plots`; -- Fig. S4 (present-day temperature and precipitation maps): links to the calendar-effects netCDF files are in the `/data/nc_files` folder; The variables plotted are `tas`, `precip`, `mtco`, and `mtwa`; -- Fig. S8 (pseudo-daily interpolation plots): in the folder `/pseudo-daily_plots` -- Fig. S9 (interpolation error maps): links to the calendar-effects netCDF files are in the `/data/nc_files` folder; The variables plotted are `xm_linear_error` and `xm_harmonic_error`. \ No newline at end of file +- Figs. 1-5 and 7-9 (month-length plots): in the folder `/month_length_plots`; +- Figs. 11-13 (calendar-effect maps): links to the calendar-effects netCDF files are in the `/data/nc_files` folder; The variables plotted are `xm_harmonic_ltmdiff` (Figs. 11 and 13), `mtco_ltmdiff` and `mtwa_ltmdiff` (Fig. 12); +- Fig. 14 (TraCE plots); in the folder `/TraCE_plots`; +- Fig. 6 (orbital-parameter plots): in the folder `/orb_param_plots`; +- Fig. 10 (present-day temperature and precipitation maps): links to the calendar-effects netCDF files are in the `/data/nc_files` folder; The variables plotted are `tas`, `precip`, `mtco`, and `mtwa`; +- Fig. 15 (pseudo-daily interpolation plots): in the folder `/pseudo-daily_plots` +- Fig. 16 (interpolation error maps): links to the calendar-effects netCDF files are in the `/data/nc_files` folder; The variables plotted are `xm_linear_error` and `xm_harmonic_error`. \ No newline at end of file diff --git a/data/figure_data/month_length_plots/FigS03_PMIP4_cal_noleap_insol_45s_anm.csv b/data/figure_data/month_length_plots/Fig05_PMIP4_cal_noleap_insol_45s_anm.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS03_PMIP4_cal_noleap_insol_45s_anm.csv rename to data/figure_data/month_length_plots/Fig05_PMIP4_cal_noleap_insol_45s_anm.csv diff --git a/data/figure_data/month_length_plots/FigS03_PMIP4_cal_noleap_insol_45s_anm_colors.csv b/data/figure_data/month_length_plots/Fig05_PMIP4_cal_noleap_insol_45s_anm_colors.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS03_PMIP4_cal_noleap_insol_45s_anm_colors.csv rename to data/figure_data/month_length_plots/Fig05_PMIP4_cal_noleap_insol_45s_anm_colors.csv diff --git a/data/figure_data/month_length_plots/FigS05_PMIP4_cal_noleap_insol_45n_noadj_diff.csv b/data/figure_data/month_length_plots/Fig07_PMIP4_cal_noleap_insol_45n_noadj_diff.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS05_PMIP4_cal_noleap_insol_45n_noadj_diff.csv rename to data/figure_data/month_length_plots/Fig07_PMIP4_cal_noleap_insol_45n_noadj_diff.csv diff --git a/data/figure_data/month_length_plots/FigS05_PMIP4_cal_noleap_insol_45n_noadj_diff_colors.csv b/data/figure_data/month_length_plots/Fig07_PMIP4_cal_noleap_insol_45n_noadj_diff_colors.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS05_PMIP4_cal_noleap_insol_45n_noadj_diff_colors.csv rename to data/figure_data/month_length_plots/Fig07_PMIP4_cal_noleap_insol_45n_noadj_diff_colors.csv diff --git a/data/figure_data/month_length_plots/FigS06_PMIP4_cal_noleap_insol_eq_noadj_diff.csv b/data/figure_data/month_length_plots/Fig08_PMIP4_cal_noleap_insol_eq_noadj_diff.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS06_PMIP4_cal_noleap_insol_eq_noadj_diff.csv rename to data/figure_data/month_length_plots/Fig08_PMIP4_cal_noleap_insol_eq_noadj_diff.csv diff --git a/data/figure_data/month_length_plots/FigS06_PMIP4_cal_noleap_insol_eq_noadj_diff_colors.csv b/data/figure_data/month_length_plots/Fig08_PMIP4_cal_noleap_insol_eq_noadj_diff_colors.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS06_PMIP4_cal_noleap_insol_eq_noadj_diff_colors.csv rename to data/figure_data/month_length_plots/Fig08_PMIP4_cal_noleap_insol_eq_noadj_diff_colors.csv diff --git a/data/figure_data/month_length_plots/FigS07_PMIP4_cal_noleap_insol_45s_noadj_diff.csv b/data/figure_data/month_length_plots/Fig09_PMIP4_cal_noleap_insol_45s_noadj_diff.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS07_PMIP4_cal_noleap_insol_45s_noadj_diff.csv rename to data/figure_data/month_length_plots/Fig09_PMIP4_cal_noleap_insol_45s_noadj_diff.csv diff --git a/data/figure_data/month_length_plots/FigS07_PMIP4_cal_noleap_insol_45s_noadj_diff_colors.csv b/data/figure_data/month_length_plots/Fig09_PMIP4_cal_noleap_insol_45s_noadj_diff_colors.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS07_PMIP4_cal_noleap_insol_45s_noadj_diff_colors.csv rename to data/figure_data/month_length_plots/Fig09_PMIP4_cal_noleap_insol_45s_noadj_diff_colors.csv diff --git a/data/figure_data/month_length_plots/FigS02_PMIP4_cal_noleap_insol_eq_anm.csv b/data/figure_data/month_length_plots/Fig09_PMIP4_cal_noleap_insol_eq_anm.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS02_PMIP4_cal_noleap_insol_eq_anm.csv rename to data/figure_data/month_length_plots/Fig09_PMIP4_cal_noleap_insol_eq_anm.csv diff --git a/data/figure_data/month_length_plots/FigS02_PMIP4_cal_noleap_insol_eq_anm_colors.csv b/data/figure_data/month_length_plots/Fig09_PMIP4_cal_noleap_insol_eq_anm_colors.csv similarity index 100% rename from data/figure_data/month_length_plots/FigS02_PMIP4_cal_noleap_insol_eq_anm_colors.csv rename to data/figure_data/month_length_plots/Fig09_PMIP4_cal_noleap_insol_eq_anm_colors.csv diff --git a/data/figure_data/orb_param_plots/PMIP_orb_elt_events_150ka_1kyr.csv b/data/figure_data/orb_param_plots/Fig06_PMIP_orb_elt_events_150ka_1kyr.csv similarity index 100% rename from data/figure_data/orb_param_plots/PMIP_orb_elt_events_150ka_1kyr.csv rename to data/figure_data/orb_param_plots/Fig06_PMIP_orb_elt_events_150ka_1kyr.csv diff --git a/data/figure_data/pseudo_daily_plots/FigS08.dat b/data/figure_data/pseudo_daily_plots/Fig15.dat similarity index 100% rename from data/figure_data/pseudo_daily_plots/FigS08.dat rename to data/figure_data/pseudo_daily_plots/Fig15.dat diff --git a/figures/FigS02_InsolDiff_Eq.pdf b/figures/Fig04_InsolDiff_Eq.pdf similarity index 100% rename from figures/FigS02_InsolDiff_Eq.pdf rename to figures/Fig04_InsolDiff_Eq.pdf diff --git a/figures/FigS03_InsolDiff_45s.pdf b/figures/Fig05_InsolDiff_45s.pdf similarity index 100% rename from figures/FigS03_InsolDiff_45s.pdf rename to figures/Fig05_InsolDiff_45s.pdf diff --git a/figures/FigS01_OrbitalParams.pdf b/figures/Fig06_OrbitalParams.pdf similarity index 100% rename from figures/FigS01_OrbitalParams.pdf rename to figures/Fig06_OrbitalParams.pdf diff --git a/figures/FigS05_InsolAnm_45n.pdf b/figures/Fig07_InsolAnm_45n.pdf similarity index 100% rename from figures/FigS05_InsolAnm_45n.pdf rename to figures/Fig07_InsolAnm_45n.pdf diff --git a/figures/FigS06_Insol_anm_eq.pdf b/figures/Fig08_Insol_anm_eq.pdf similarity index 100% rename from figures/FigS06_Insol_anm_eq.pdf rename to figures/Fig08_Insol_anm_eq.pdf diff --git a/figures/FigS07_InsolAnm_45s.pdf b/figures/Fig09_InsolAnm_45s.pdf similarity index 100% rename from figures/FigS07_InsolAnm_45s.pdf rename to figures/Fig09_InsolAnm_45s.pdf diff --git a/figures/FigS04_Modern_tas_pr.pdf b/figures/Fig10_Modern_tas_pr.pdf similarity index 100% rename from figures/FigS04_Modern_tas_pr.pdf rename to figures/Fig10_Modern_tas_pr.pdf diff --git a/figures/Fig04_CalEffect_tas.pdf b/figures/Fig11_CalEffect_tas.pdf similarity index 100% rename from figures/Fig04_CalEffect_tas.pdf rename to figures/Fig11_CalEffect_tas.pdf diff --git a/figures/Fig05_CalEffect_mtwa_mtco.pdf b/figures/Fig12_CalEffect_mtwa_mtco.pdf similarity index 100% rename from figures/Fig05_CalEffect_mtwa_mtco.pdf rename to figures/Fig12_CalEffect_mtwa_mtco.pdf diff --git a/figures/Fig06_CalEffect_pr.pdf b/figures/Fig13_CalEffect_pr.pdf similarity index 100% rename from figures/Fig06_CalEffect_pr.pdf rename to figures/Fig13_CalEffect_pr.pdf diff --git a/figures/Fig07_Transient.pdf b/figures/Fig14_Transient.pdf similarity index 100% rename from figures/Fig07_Transient.pdf rename to figures/Fig14_Transient.pdf diff --git a/figures/FigS08_DailyInterp.pdf b/figures/Fig15_DailyInterp.pdf similarity index 100% rename from figures/FigS08_DailyInterp.pdf rename to figures/Fig15_DailyInterp.pdf diff --git a/figures/FigS09_InterpEffects.pdf b/figures/Fig16_InterpEffects.pdf similarity index 100% rename from figures/FigS09_InterpEffects.pdf rename to figures/Fig16_InterpEffects.pdf diff --git a/figures/README.md b/figures/README.md index 25050d3..c469bb0 100644 --- a/figures/README.md +++ b/figures/README.md @@ -1,37 +1,36 @@ Figure Captions --------------- -**Figure 1:** Variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar, shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. The month-length "anomalies" or differences from the present-day are shown by shading, with individual paleo months that are shorter than those at present indicated by green shades and those that are longer indicated by blue shades. The day that perihelion occurs for each 1 kyr interval is indicated by a magenta dot, and the overall pattern of month-length anomalies can be seen to follow the day of perihelion. +**Figure 1:** Variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar, shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. The month-length "anomalies" or differences from the present-day are shown by shading, with individual paleo months that are shorter than those at present indicated by green shades and those that are longer indicated by blue shades. The day that perihelion occurs for each 1 kyr interval is indicated by a magenta dot, and the overall pattern of month-length anomalies can be seen to follow the day of perihelion. The figure shows that the changing month lengths move the beginning, middle and ending days of each month (as well as the beginning and ending days of the year). -**Figure 2:** As in Fig. 1, but with shading showing the variations in the difference (in days) between the mid-month day of each month and the day of the June solstice. Months that are shifted closer to the June solstice are indicated by orange hues while those that are farther away are indicated by blue. Variations in the beginning and ending days of individual months can be seen to track the climatic precession parameter (*e*∙*sin* ω, where *e* is eccentricity and ω is the longitude of perihelion measured from the vernal equinox, an index of Earth's distance from the Sun at the summer solstice), which is plotted at the right side of the figure (red dots). (Note that the inverse of the climatic precession parameter is plotted for easier comparison.) +**Figure 2:** Variations in the difference (in days) between the mid-month day of each month and the day of the June solstice. Months that are shifted closer to the June solstice are indicated by orange hues while those that are farther away are indicated by blue. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. Variations in the beginning and ending days of individual months can be seen to track the climatic precession parameter (e∙sin ω, where e is eccentricity and ω is the longitude of perihelion measured from the vernal equinox, an index of Earth's distance from the Sun at the summer solstice), which is plotted at the right side of the figure (red dots). (Note that the inverse of the climatic precession parameter is plotted for easier comparison.) -**Figure 3:** As in Fig.1, but with shading showing calendar effects on insolation at 45° N. The differences plotted show the values of average daily insolation at mid-month days identified using the appropriate fixed-angular paleo calendar minus those using the fixed-length definition of present-day months, with orange hues showing positive difference, and purple hues negative. Figs. S3 and S4 show differences for the equator and 45° S. +**Figure 3:** Calendar effects on insolation at 45° N. The differences plotted show the values of average daily insolation at mid-month days identified using the appropriate fixed-angular paleo calendar minus those using the fixed-length definition of present-day months, with orange hues showing positive difference, and purple hues negative. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. -**Figure 4:** Calendar effects on near-surface air temperature for 6 ka (upper left), 97 ka (upper right), 127 ka (lower left) and 116 ka (lower right). The maps show the patterns of month-length adjusted average temperatures minus the unadjusted values, using 1981-2010 long-term averages of CFSR *tas* values, with positive difference (indicating that the adjusted data would be warmer than unadjusted data) in red hues, and negative differences in blue. +**Figure 4:** Calendar effects on insolation at the equator. The differences plotted show the values of average daily insolation at mid-month days identified using the appropriate fixed-angular paleo calendar minus those using the fixed-length definition of present-day months, with orange hues showing positive difference, and purple hues negative. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. -**Figure 5:** Calendar effects on the mean near-surface air temperatures of the warmest (MTWA) and coldest (MTCO) months and their differences (an index of seasonality) for 6 ka, 97 ka, 116 ka and 127 ka (top to bottom row). The maps show the patterns of month-length adjusted average temperatures minus the unadjusted values for MTWA and MTCO, using 1981-2010 long-term averages of CFSR **tas** values, with positive difference (indicating that the adjusted data would be warmer than unadjusted data) in red hues, and negative differences in blue. +**Figure 5:** Calendar effects on insolation at 45° S. The differences plotted show the values of average daily insolation at mid-month days identified using the appropriate fixed-angular paleo calendar minus those using the fixed-length definition of present-day months, with orange hues showing positive difference, and purple hues negative difference. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. -**Figure 6:** Calendar effects on precipitation rate for 6 ka (upper left), 97 ka (upper right), 127 ka (lower left) and 116 ka (lower right). The maps show the patterns of month-length adjusted precipitation rate minus the unadjusted values, using 1981-2010 long-term averages of CMAP *precip* values, with positive difference (indicating that the adjusted data would be wetter than unadjusted data) in blue hues, and negative differences in brown. +**Figure 6:** Orbital parameter variations at 1 kyr intervals over the past 150 kyr for obliquity, climatic precession, eccentricity, and day of perihelion (relative to January 1). Climatic precession is calculated as e ⋅ sin(ω), where e is eccentricity and ω is the longitude of perihelion measured from the vernal equinox. -**Figure 7:** Time series of original and month-length-adjusted annual area-weighted averages of TraCE-21k data (Liu et al., 2009), expressed as difference from the 1961-1989 long-term mean for (a-c) 2 m air temperature, (d) precipitation rate, and (e-f) precipitation minus evaporation (P - E). The original or unadjusted data are plotted in gray and black, and the adjusted data in colors. The area averages are grid-cell area-weighted values for land grid points in each region, and the smoother curves are locally weighted regression curves with a window half-width of 100 years. The regions are defined as: (a) 15 to 75° N and ‑170 to 60° E, (b) 10 to 50° S and 110 to 160° E, (c) global ice-free land area, (d) 0 to 30° N and ‑30 to 120° E, (e) 5 to 17° N and ‑5 to 30° E, and (f) 31 to 43° N and -5 to 30° E. +**Figure 7:** Long-term differences in mid-month average daily insolation relative to present (0 ka or 1950 CE) at 45° N for a fixed-angular calendar. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. -Supplemental Figure Captions ----------------------------- +**Figure 8.** Long-term differences in mid-month average daily insolation relative to present (0 ka or 1950 CE) at the equator for a fixed-angular calendar. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. -**Figure S1**: Orbital parameter variations at 1 kyr intervals over the past 150 kyr for obliquity, climatic precession, eccentricity, and day of perihelion (relative to January 1). Climatic recession is calculated as e ⋅ sin(ω), where e is eccentricity and ω is the longitude of perihelion measured from the vernal equinox. +**Figure 9.** Long-term differences in mid-month average daily insolation relative to present (0 ka or 1950 CE) at 45° S for a fixed-angular calendar. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. -**Figure S2:** The shading shows the calendar effects on insolation at the equator. The differences plotted show the values of average daily insolation at mid-month days identified using the appropriate fixed-angular paleo calendar minus those using the fixed-length definition of present-day months, with orange hues showing positive difference, and purple hues negative. Figs. 3 and S3 show differences for 45° N and 45° S. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. +**Figure 10.** Present-day (1981-2010 CE) long-term mean values of monthly near-surface air temperature (tas) from the Climate Forecast System Reanalysis (CFSR), the mean temperatures of the warmest and coldest months and their differences from the same data, and precipitation rate (precip) from the CPC Merged Analysis of Precipitation (CMAP). -**Figure S3:** The shading shows the calendar effects on insolation at 45° S. The differences plotted show the values of average daily insolation at mid-month days identified using the appropriate fixed-angular paleo calendar minus those using the fixed-length definition of present-day months, with orange hues showing positive difference, and purple hues negative. Figs. 3 and S2 show differences for 45° N and the equator. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. +**Figure 11**. Calendar effects on near-surface air temperature for 6 ka (upper left), 97 ka (upper right), 127 ka (lower left) and 116 ka (lower right). The maps show the patterns of month-length adjusted average temperatures minus the unadjusted values, using 1981-2010 long-term averages of CFSR *tas* values, with positive difference (indicating that the adjusted data would be warmer than unadjusted data) in red hues, and negative differences in blue. -**Figure S4:** Present-day (1981-2010 CE) long-term mean values of monthly near-surface air temperature (*tas*) from the Climate Forecast System Reanalysis (CFSR), the mean temperatures of the warmest and coldest months and their differences from the same data, and precipitation rate (*precip*) from the CPC Merged Analysis of Precipitation (CMAP). +**Figure 12.** Calendar effects on the mean near-surface air temperatures of the warmest (MTWA) and coldest (MTCO) months and their differences (an index of seasonality) for 6 ka, 97 ka, 116 ka and 127 ka (top to bottom row). The maps show the patterns of month-length adjusted average temperatures minus the unadjusted values for MTWA and MTCO, using 1981-2010 long-term averages of CFSR tas values, with positive difference (indicating that the adjusted data would be warmer than unadjusted data) in red hues, and negative differences in blue. -**Figure S5:** The shading shows the long-term differences in mid-month average daily insolation relative to present (0 ka or 1950 CE) at 45° N for a fixed-angular calendar. Figs. S6 and S7 show differences for the equator and 45° S. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. +**Figure 13.** Calendar effects on precipitation rate for 6 ka (upper left), 97 ka (upper right), 127 ka (lower left) and 116 ka (lower right). The maps show the patterns of month-length adjusted precipitation rate minus the unadjusted values, using 1981-2010 long-term averages of CMAP *precip* values, with positive difference (indicating that the adjusted data would be wetter than unadjusted data) in blue hues, and negative differences in brown. -**Figure S6:** The shading shows the long-term differences in mid-month average daily insolation relative to present (0 ka or 1950 CE) at the equator for a fixed-angular calendar. Figs. S5 and S7 show differences for 45° N and 45° S. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. +**Figure 14.** Time series of original and month-length-adjusted annual area-weighted averages of TraCE-21k data (Liu et al., 2009), expressed as difference from the 1961-1989 long-term mean for (a-c) 2 m air temperature, (d) precipitation rate, and (e-f) precipitation minus evaporation (P - E). The original or unadjusted data are plotted in gray and black, and the adjusted data in colors. The area averages are grid-cell area-weighted values for land grid points in each region, and the smoother curves are locally weighted regression curves with a window half-width of 100 years. The regions are defined as: (a) 15 to 75° N and 170 to 60° E, (b) 10 to 50° S and 110 to 160° E, (c) global ice-free land area, (d) 0 to 30° N and 30 to 120° E, (e) 5 to 17° N and 5 to 30° E, and (f) 31 to 43° N and 5 to 30° E. -**Figure S7:** The shading shows the long-term differences in mid-month average daily insolation relative to present (0 ka or 1950 CE) at 45° S for a fixed-angular calendar. Figs. S5 and S6 show differences for 45° N and the equator. As in Fig. 1, variations over the past 150 kyr in the beginning and ending days of fixed-angular months for a 365-day "noleap" calendar are shown for 1 kyr intervals beginning at 0 ka (1950 CE). The left side of each horizontal bar shows the beginning day while the right side shows the ending day of a particular month for each 1 kyr interval. +**Figure 15.** Pseudo-daily interpolated temperature (top row) and precipitation (bottom row) for some representative locations: (a, c) Madison, Wisconsin, USA, (b) Australia, and (d) the Indian Ocean. The original monthly mean data are shown by the black dots and stepped curves (black lines), daily values linearly interpolated between the monthly mean values are shown in blue, and daily values using the mean-preserving approach of Epstein (1991) are shown in red. The annual interpolation error (or the difference between the annual average calculated using the original data and the pseudo-daily interpolated data) is given for the mean-preserving approach in each case. The interpolated data for this figure were generated using the program `demo_01_pseudo_daily_interp.f90`. + +**Figure 16.** Pseudo-daily interpolation errors for CFSR near-surface air temperature (left-hand column) and CMAP precipitation rate (right-hand column). The top set of maps shows the interpolation errors, or the differences between the original monthly mean values and the monthly mean values recalculated from linear interpolation of pseudo-daily values. The bottom set of maps shows the interpolation errors for mean-preserving (Epstein, 1991) interpolation. -**Figure S8:** Pseudo-daily interpolated temperature (top row) and precipitation (bottom row) for some representative locations:** (a, c) Madison, Wisconsin, USA, (b) Australia, and (d) the Indian Ocean. The original monthly mean data are shown by the black dots and stepped curves (black lines), daily values linearly interpolated between the monthly mean values are shown in blue, and daily values using the mean-preserving approach of Epstein (1991) are shown in red. The annual interpolation error (or the difference between the annual average calculated using the original data and the pseudo-daily interpolated data) is given for the mean-preserving approach in each case. The interpolated data for this figure was generated using the program `demo_01_pseudo_daily_interp.f90`. -**Figure S9:** Pseudo-daily interpolation errors for CFSR near-surface air temperature (left-hand column) and CMAP precipitation rate (right-hand column). The top set of maps shows the interpolation errors, or the differences between the original monthly mean values and the monthly mean values recalculated from linear interpolation of pseudo-daily values. The bottom set of maps shows the interpolation errors for mean-preserving (Epstein, 1991) interpolation.