GCEM Model output with WTG approximation in place

12/19/05
SST = 30, 1 -day
* Fixed the moisture offset
12/14/05
SST = 30
* Moisture offset caused by problem with Surface Latent Heat Flux
  • Both panels show Dqdt (magenta line) from the current 60-day run.
  • In the top panel the sum of terms (blue line) uses the Net Condensation and Large Scale Forcing from the 60-day run and the Surface Latent Heat Flux from the 15-day run.
  • In the bottom panel, the terms in the sum (Blue line) are ALL from the 60-day run. Thus, the Surface LHF must be creating the offset.

    12/13/05
    SST = 30
    * Looking into the moisture offset Comparing the difference between the terms Dqdt, -Netcond , LSF and SurfLHF in the 15 day run to the 30 day run, (15-day-run MINUS the first 15 days of the 30-day-run.).
    There are differences in all of the components in the first 15 days, but in the Surface LHF the difference is evident from the beginning. In the first timestep we can't attribute the differences to numerical error accumulating during the run.

    SST = 29.75 (ext=12.13.05) 60 days
    * Timeseries of Moisture Budget Terms (mm/hr) Increments Looks like there is an off-set in the bottom panel

  • Mean Dqdt = -0.0017736 std dev = 0.17617
  • Mean of sum of terms = 0.19274 std dev = 0.038639
  • Mean difference between curves is -0.19452
  • Correlation between the curves is 0.9767
    * Rainrate and Net Condensation Looks good!
  • Mean Netcond = 0.47904 std dev = 0.29421
  • Mean rainrate = 0.48002 std dev = 0.29326
  • Mean difference between curves is 0.0014139
    * Timeseries of Temperature Budget Terms (C/day) Increments Looks good!
  • Mean DTdt = 0.001105 std dev = 0.049457
  • Mean of sum of terms = -0.00056999 std dev = 0.050519
  • Mean difference between curves is 0.001675

    12/12/05
    SST = 30.0 (ext=12.10.05) 60 days
    * Timeseries of Moisture Budget Terms (mm/hr) Increments Looks like there is an off-set in the bottom panel

  • Mean Dqdt = 0.015714 std dev = 0.17677
  • Mean of sum of terms (blue line in bottom panel) = 0.17205 std dev = 0.067115
  • Mean difference between curves is -0.15634
  • Correlation between the curves is 0.9315
    * Rainrate and Net Condensation Looks good!
  • Mean Netcond = 1.2619 std dev = 0.67248
  • Mean rainrate = 1.2839 std dev = 0.69487
  • Mean difference between curves is 0.023113
    * Timeseries of Temperature Budget Terms (C/day) Increments Looks good!
  • Mean DTdt = 0.0022088 std dev = 0.049549
  • Mean of sum of termsv (black line in bottom panel) = 0.0038729 std dev = 0.050886
  • Mean difference between curves is -0.0016641

    12/08/05
    SST = 30.0 (ext=11.03.05) 15 days
    * Accumulated Moisture Budget Terms Divergence after day 150 (day 6)
    * Accumulated Moisture Budget Terms/Time Elapsed in hours NOT a big difference once you divide by the elapsed time
    * Time series: Increments (which are shown as "accumulated" above) Moisture Budget Terms Nice agreement here.

  • Mean Dqdt = 0.039986; std dev = 0.18021
  • Mean of sum of terms = 0.019172; std dev = 0.025241
  • Mean difference between curves is 0.020814
  • Correlation between the curves is 0.9904
    * Rainrate and condensation time series Beautiful agreement!
  • Mean Netcond = 0.35577 std dev = 0.32156
  • Mean rainrate = 0.34512 std dev = 0.30275
  • Mean difference between curves is -0.0097493

    * Accumulated Temperature Budget Terms Some divergence after hour 100 (day 4)
    * Time series: Increments (which are shown as "accumulated" above) Temperature Budget Terms Overlapping lines in bottom panel plot

  • Mean DTdt = 0.0053673 std dev = 0.056737
  • Mean of sum of terms = 0.0066522 std dev = 0.056968
  • Mean difference between curves is -0.0012849

    12/01/05
    SST = 28.0 (ext=11.29.05) 14 days
    Accumulated values in the budgets plotted over time:
    * Moisture Budget Terms **Compare
    * Temperature Budget Terms **Compare


    11/21/05
    SST = 29.0 (ext=11.21.05A) 3 days
    Moisture Budget
    * Time series of changes in the accumulated values
    * Horizontally Averaged Rainrate with moisture budget terms
    * Accumulated values in the moisture budget plotted over time, as it is accumulating **Compare
    Temperature Budget
    * Time series of changes in the accumulated values
    * Accumulated values plotted over time **Compare

    11/15/05
    SST = 29.5 (ext=11.15.05)
    * Spatial Mean rain info
    * Time mean rain info
    11/02/05
    * Total Precip in [mm] (ext=10.26.05)
    * Two Curves in [mm/hr]: Accumulated Hourly Precip. total differenced and Rainrate values output from the model (ext=10.26.05)
    * Net condensation and Rainrate [mm/hr] SST = 30, 15 days

    11/01/05

    * Corrected Moisture Budget * **Compare

  • Changed value of sampling variable to match model timestep: ndt_stat = dt
  • Fifteen day run; SST = 30 (ext=10.26.05)

  • This has been confusing to me because of all the different averages and because of our sampling.
  • In this moisture budget graphic the top panel shows all values and the bottom panel shows the two sides of the equation which ought to balance.
  • The values are in W/m2 and they are the TIME-EVOLVING AVERAGE value of each term over the domain (both horizontal and vertical).
  • So the "time series" is the evolution of our knowledge about the domain-average value give that we have sampled for X number of days.

    For example:

    At day 5, the domain averaged value in W/m2 of dq/dt is about 7.8 W/m2. That is an average over the 5 days that have passed.
    If we had stopped running the model at 3 days that value would have been -14 W/m2.
    If we keep running and then stop at day 10 the average value is 27 W/m2.
  • What I was plotting before was the change in our ESTMATED value of the average given the length of time that the model had been running.
    10/31/05

    Changed value of sampling variable to match model timestep: ndt_stat = dt
    Fifteen day run; SST = 30 (ext=10.26.05)
    * Moisture Budget

    * Temperature Budget
    * Corrected Moisture Budget (same as the moisture budget on 11/01/05.)
    * Corrected Temperature Budget

    10/28/05

    Changed value of sampling variable to match model timestep: ndt_stat = dt
    Three day run; SST = 29.5
    * Moisture Budget
    Changing ndt_stat = dt from 300 seconds to the 12 second model time step does not improve the model error in the moisture budget.
    * Temperature Budget
    This looks fine. As before, the cumulative average error in the final step is of the order 10 -1 W/m2.
    * Corrected Moisture Budget **Compare
    * Corrected Temperature Budget

    10/25/05

    1. No negative q Six day run; SST = 29.5
    The following plots were made with results I obtained while visting NASA/GSFC with Chung-Lin Shie. The run was for 6 days. We used the file called "data", which is the original output file of the GCEM code. We used his code "plot.f" to calculate the moisture and temperature budgets.

    * Moisture Budget
    The moisture budget does not balance. There is a clear offset in the bottom panel (figure above) between the local time rate of change in water vapor and the large scale forcing + latent heat flux at the surface - the net condensation (this last term is the collection of effects of all microphysical processes: deposition, freezing, sublimation ...).
    * Corrected Moisture Budget

    * Temperature Budget
    The temperature budget looks great.
    * Corrected Temperature Budget

    2. Negative q allowed Six day run; SST = 29.5
    The following plots were made with results I obtained today 10/25/05. The run was for 6 days. I used the file called "data_10.25.05", which is the output file of GCEM code "/home/cristina/GCEM/GCEM_orig_moisturecode.f". This code I used the code "/home/cristina/GCEM/plotbudgets/plot.f" from the NASA folks to calculate the moisture and temperature budgets.

    * Moisture Budget
    The moisture budget does not balance. There is a clear offset in the bottom panel (figure above) between the local time rate of change in water vapor and the large scale forcing + latent heat flux at the surface - the net condensation (this last term is the collection of effects of all microphysical processes: deposition, freezing, sublimation ...).
    * Corrected Moisture Budget

    * Temperature Budget
    The temperature budget looks great.
    * Corrected Temperature Budget

    09/13/05

    SST = 29

  • MSE
  • DSE
  • DSE error (imbalance)
  • moisture equation
    35 - 46 = -9 ?=? 23 W/m2

    SST = 29.5

  • MSE
  • DSE
  • DSE error (imbalance)
  • moisture equation
    80 - 55 ?=? 32 W/m2

    SST = 30

  • MSE
  • DSE
  • DSE error (imbalance)
  • moisture equation
    -40 - 345 ?=? 269 W/m2
    C-.L. suggests that saving the modelled values at every hour as I do is not sufficient to resolve the budget.
    They use the values every 120 seconds.

    08/04/05
    * WTG vertical velocity , MSE, DSE, rainrate (time-mean, mass-weighted, vertically integrated WTG vertical velocity)
    * Same as above but normalized with respective values at SST 28.5
    * Normalized and on the same plot (normalized by their respective values at SST 28.5)

    08/03/05
    Mean difference (last 30 days)
    SST [C] MSE - Evap - RC + d([rho h])/dt [ W m -2]
    28 52.1371
    28.5 59.7995
    29 62.1700
    29.5 80.1406
    29.75 116.8909
    30 510.9965
    30.5

    08/02/05

    Time Series of various vertically integrated quantities in W m -2
    SST = 28
    * Radiative Cooling
    * Evaporation
    * Evaporation plus Radiative Cooling
    * All of the above
    * overplotted l.h.s., r.h.s.: MSE = Evaporation + Radiative Cooling - d([rho h])/dt
    * ZOOM on plot above
    * Precipitation

    SST = 28.5
    * Radiative Cooling
    * Evaporation
    * Evaporation plus Radiative Cooling
    * All
    * overplotted l.h.s., r.h.s.: MSE = Evaporation + Radiative Cooling - d([rho h])/dt
    * Precipitation

    SST = 29
    * Radiative Cooling
    * Evaporation
    * Evaporation plus Radiative Cooling
    * All
    * overplotted l.h.s., r.h.s.: MSE = Evaporation + Radiative Cooling - d([rho h])/dt
    * Precipitation

    SST = 29.5
    * Radiative Cooling
    * Evaporation
    * Evaporation plus Radiative Cooling
    * All
    * overplotted l.h.s., r.h.s.: MSE = Evaporation + Radiative Cooling - d([rho h])/dt
    * Precipitation

    SST = 29.75
    * Radiative Cooling
    * Evaporation
    * Evaporation plus Radiative Cooling
    * All
    * overplotted l.h.s., r.h.s.: MSE = Evaporation + Radiative Cooling - d([rho h])/dt
    * Precipitation

    SST = 30
    * Radiative Cooling
    * Evaporation
    * Evaporation plus Radiative Cooling
    * All
    * overplotted l.h.s., r.h.s.: MSE = Evaporation + Radiative Cooling - d([rho h])/dt
    * Precipitation

    07/29/05

    Moisture Budget balance (Question 3) need to write more explanation here.
    * SST = 28
    * SST = 28.5
    * SST = 29.5

    07/22/05

    * Medians of rainrate and evaporation: FINAL 30 days of 60 day run
    Median values from graph above
    SST [C] rain [mm/day] evap [mm/day]
    28 3.0383 4.1840
    28.5 5.6022 4.1918
    29 6.5121 3.9576
    29.5 8.3520 4.9444
    29.75 15.3966 4.1942
    30 44.1405 4.0388
    30.5 52.9762 4.4032

    Mean values of rainrate and evaporation
    SST [C] rain [mm/day] evap [mm/day]
    28 3.4224 4.1602
    28.5 5.8258 4.1960
    29 6.9264 3.9840
    29.5 8.6501 4.9470
    29.75 15.6944 4.1525
    30 44.3572 4.0408
    30.5 53.2073 4.3973

    * Boxplots rainrate: FINAL 30 days of 60 day run
    The spread (variance or IQR is shown here) is much smaller now for the two rainiest cases. Without the values from the first 30 days, we have a steady heavy rain in SST = 30 and SST = 30.5 cases.

    06/03/05

    * Rainrate time series with Radiative Cooling time series and correlation coefficients SST = 28, ..., 30.5

    05/19/05-05/20/05
    * Wwtg with and without density weighting for SST = 28 and 28.5 C
    * Wwtg without density weighting for SST = 28 and 28.5 C
    * Wwtg with density weighting for all SST cases

    * Precipitation and Evapoation time series for SST = 28 and 28.5
    * GDS (green circles) and GMS (blue dots) for all SST cases.
    * Ratio of GDS to GMS
    * Density of moist air (at model's pressure level and a sample temp. structure)


    05/17/05

    Revisions to WTG paper 1
     Resolving once and for all the possibility of power at specific frequencies of the result of the GCEM.

    First the RCE case (90 days at SST = 28C)
    The following are a set of the Maximum Entropy Spectrum (MEM) of the same long (90-day, hourly) time series or rain rates divided into sections and then transformed into power spectra.
    * First and Second halves of rainrate time series
    * Four quarters of rainrate time series with the mean of the four
    * Four quarters with First and Second halves
    Significant power is between 8 and 10 hours. I say significant because that peak in the power persists through all of the pieces of the time series, becoming more potent in the later parts of the time series.

    MEM of First and Second halves of WTG run with...
    * SST = 28
    * SST = 28.5
    * SST = 29

    MEM of 4 quarters (and mean spectrum) of WTG run with...
    * SST = 28.5
    * SST = 29
    * SST = 29.75

    * MEM of quarterly rainrates for RCE and SST = 28,28.5,29 and 29.75

    05/11/05

    Revisions to WTG paper 1
     * SST = 28
    * SST = 28.5
    * SST = 29.75

    05/10/05

    Revisions to WTG paper 1
     * I've plotted two SST cases to address Chris' comment (G2) on the evaporation and rainrate in the paper's figure 14 in which P=E for SST = 28.5 and not for SST = 28. Why is P not equal to E for the case in which SST = 28, the SST for which we evaluated RCE?
    In the following figures, I plot the daily time series for

    • Wwtg, vertically integrated to TOA (blue dot) and tropopause (magenta circle)
    • evaporation (mm/day) (various colors for all cases, see legend)
    * SST = 28
    * zoomed in on SST = 28
    * SST = 28.5

    * Evaporation time series for RCE with SST = 28
    * Evaporation time series for ALL SST
    There is a prolonged period of evaporation for the case where SST = 28 that I don't understand yet.

    Must test the mean. perhaps it is influenced by the time period that we take??
    (SST , mean evaporation over the total 60 days):

    • (28, 4.5267)
    • (28.5, 4.2775)
    • (29, 4.1811 )
    • (29.5, 4.6183 )
    • (29.75, 3.9814 )
    • (30., 3.8588 )
    • (30.5, 4.2792)

    Time series of the mean (vertically integrated and weighted) WTG vertical velocity for the cases without shear.

    • Top panel is zoomed in on the final 30 days
    • 2nd panel shows total 60 days
    • 3rd panel shows positive values from the 60 days
    • bottom panel shows negative values from the 60 days
    * SST = 28 C
    * SST = 28.5 C
    * SST = 29 C
    * SST = 29.5 C
    * SST = 29.75 C
    * SST = 30 C
    * SST = 30.5 C

    Revisions to WTG paper 1
     Cases without shear: (from the first paper)
    Now have the moist air density weighting for the MSE, h, and density of dry air for the DSE, s. Concerned with the proper method of integration. Integrating over height or pressure doesn't matter because you are taking the numerical derivative over either dp or dz (both of which are not constant valued since our model vertical domain is on a stretched coordinate grid system), but then you integrate over that same variable. So you effectively cancel out whichever coordinate you choose. All that matters is WTG vertical velocity and the Δ h or Δ s.
    Plots of Gross Dry Stability/Gross Moist Stability from the same experiments but with one difference: choice of which side to begin the integration
    * from the right, higher height level, lower pressure
    * from the left, lower height level, higher pressure
    * The values are slightly different, but the trends are the same. I think that matters more. Is this true?
    Used MatLab script ~/GCEM/matlab/plt_gross_moist_stab2.m

    Revisions to WTG paper 1

    04/01/05
    * Probably not right. The density is the dry air density...
    NEW Ms/M with density weighting (density of dry air at all levels) and integration with respect to dz

    03/22/05
    Precipitation results for case with linear zonal wind shear (-600 to 600 at top of troposphere)

    SST = 29C
    * Time series
    * Histogram
    * Mean rainrates (weekly and monthly)
    SST = 30C
    * Time series
    * Histogram
    * Mean rainrates (weekly and monthly)

    SST=30 with shear (bottom figures are zoomed in on the same area, where there is a cloud)
    * Figure A: Perturbation Potential temp. (colored contours) with minimum contours cloud water (white) and rain (red) at Day 41
    There is no cloud ice in this snapshot. Top panel shows a group of clouds distributed about the 100 km mark and confined below the freezing level. There is a lonely cloud at the 200 km mark. Bottom panel zooms in on this lonely cloud where there is evidence of a cloud-top cool anomaly in potential temp. and a warm anomaly inside the cloud water & rain contours.

    * Figure B: Total U and W fields at day 41
    Top two panels show the full U and W fields. The bottom two show a zoom-in on the same area which corresponds to the lonely cloud in figure A, above.
    There is some vertical shear in U on the right side of the cloud. You can see a strong updraft inside the cloud and downdrafts of similar magnitude on either side.

    03/15/05
    Tested new zonal wind shear profile.
    Performed a 5-day run with linear wind shear which stops at the tropopause.
    Wrote out many of the U wind fields to figure out what they all are exactly.

    * Time series of vertical profiles of mean U wind (UB, UB1) UB and UB1 differ on the order of 10-6 m/s.

    The next 2 snapshots in time of the wind field look the same.
    * Snapshot of full U field (umd)
    * Snapshot of full U field (UU1)

    So, compare the means to see how close umd and UU1 are at all times.
    Take time average to give a horizontal field and take a horizontal average and display over time the vertical profiles.
    These next two figures look like the same fields. They differ only by order 10-4 m/s.
    * mean umd in time and over the horizontal
    * mean UU1 in time and over the horizontal

    03/02/05-03/07/05

    Just realized that I was putting wind shear in the stratosphere!
    We originally discussed having zero wind shear above the tropopause.

    Testing linear wind shear profile
    Case SST [C] U m/s Shear? Total P [mm] Mean(P) [mm/day] Var(P) [(mm/day)^2]
    1 30 -6 No 1,885.6 31.4 308.6
    2 29 -2 No 148.0 2.4 4.0
    3 30 -2 Yes 64.1 1.1 1.9
    4 30 2 Yes 97.7 1.6 3.6

    * Mean Wwtg for 4 cases taken over final 30 days of 60 day run
    * Mean Wwtg taken over final 30 days of 60 day run
    * Rainrate and Vertical profile of Wwtg for first month (skipping the first week)
    * Vertical profile of Wwtg for final 30 days of 60 day run

    Comparing cases which both have linear windshear but opposite slopes (same magnitude)
    Precipitation time series
    * Negative Slope (easterly surface wind)
    * Positive Slope (westerly surface wind)
    Mean rain rates broken down by time interval (weekly, monthly)
    * Negative Slope (easterly surface wind)
    * Positive Slope (westerly surface wind)
    Histogram of rainrates [mm/day]
    * Negative Slope (easterly surface wind)
    * Positive Slope (westerly surface wind)

    02/15/05-02/18/05
    Variation of mean surface wind speed

    * Relative Humidity - mean vertical profiles

    * Precipitation statistics
    * Precipitation histograms

    * Wwtg: Mean vertical profiles of all cases with variable surface wind speed (-10, -6, 2, 6, 10 m/s)

    * Moist Static Energy: Time vs. Mean vertical profile for 60 days
    * Moist Static Energy: Mean vertical profile at all heights
    * Moist Static Energy: Mean vertical profile bottom 12 km of atmosphere

    * Ratio of Gross Dry stability to Moist stability
    Note the title says "SST" where is should say "mean U"

    Integrated from the surface to model top
    Gross stability parameters
    mean U [m/s] M Ms M/Ms
    -10 235.1789 698.1865 0.3368
    -6 56.9481 145.7394 0.3908
    2 7.0299 -7.5046 -0.9367
    6 59.0674 105.0757 0.5621
    10 130.8675 223.0889 0.5866

    M := Gross Moist Stability = integrated transport of vertical MSE gradients
    Ms := Gross Dry Stability = integrated transport of vertical dry static energy gradients

    Wwtg vertical velocity mean profiles with hourly rain rates:
    Note the title says "SST" where is should say "mean U"
    * U = +10 m/s (westerlies)
    * U = +6 m/s (westerlies)
    * U = +2 m/s (westerlies)
    * U = -6 m/s (easterlies)
    * U = -10 m/s (easterlies)

    10/19/04
    Gross moist stability and Gross Dry stability calculated using the 30-day mean vertical profiles of Wwtg, DSE and MSE for experiments with relaxation type 3 now called type 1 in our paper:

    Integrated from the surface to model height where the vertical velocity (Wwtg mean profile) crosses the zero-line (varies between 11 and 15 km depending on the SST):
    Gross stability parameters
    SST M Ms M/Ms
    28 7.1565 -9.4131 -0.76
    28.5 57.9296 100.2205 0.58
    29 69.0723 159.3121 0.43
    29.5 153.5161 273.3752 0.56
    29.75 321.6279 743.8150 0.43
    30 1579.5 3867.7 0.4
    30.5 1753.1 4455.6 0.4

    M := Gross Moist Stability
    Ms := Gross Dry Stability

    Integrated from the surface to model level 34 (just above 15 km for all cases, a somewhat arbitrary tropopause):
    Gross stability parameters
    SST M Ms M/Ms
    28 3.5 -13.0 -0.27
    28.5 41.2 81.6 0.50
    29 51.2 139.9 0.37
    29.5 123.5 240.7 0.51
    29.75 318.8 743.6 0.43
    30 1640.0 3928.8 0.42
    30.5 1847.0 4550.7 0.41

    M := Gross Moist Stability
    Ms := Gross Dry Stability

    10/18/04

    Integrated throughout the domain, to the top of the model:
    Gross stability parameters
    SST M Ms M/Ms
    28 12.2 -4.3 -2.8
    28.5 50.3 90.7 0.54
    29 56.9 145.7 0.39
    29.5 130.2 247.5 0.53
    29.75 294.3 719.1 0.41
    30 1439.5 3728.3 0.39
    30.5 1628.1 4331.7 0.38

    M := Gross Moist Stability
    Ms := Gross Dry Stability

    10/15/04
    * Perturbation potential temperature field at 8 hour intervals around day 41 with SST = 29.5C and
    minimum contours of rain (black) cloud ice (magenta), cloud water (white) all on the order of 10-4),
    09/16/04
    relaxation type 3
    * Perturbation potential temperature field at day 41 with minimum contours of rain (red, 2x10-4), cloud ice (black, 1x10-4), cloud water (white, 2x10-4) with SST = 29.5C
    * f(z) relaxation functions for relaxation type 1 and relaxation type 3.

    08/31/04 relaxation type 3
    * Cloud ice and cloud water with Wwtg SST ranges from 28C to 29.75C
    * Cloud ice and cloud water with Wwtg SST ranges from 28.5C to 30C

    08/30/04

    * RCE run at a new SST (29 C):
    how sensitive is the RCE of GCEM to a change in lower BC?

  • average of last 30 days of mean potential temperature profile (with reference to the RCE pt mean profile with SST = 28)
  • contour mean potential temperature profile (for the entire 90 day run)
  • movie of perturbation potential temperature profile (for the first 500 hours)
    08/25/04

    * Snapshots of the perturbation potential temperature in 2-D model domain
    relaxation type 3
    Can see waves propagate in the vertical!

  • SST = 28.5
  • SST = 29.5
  • As above but with alternate colormap

    Confidence intervals are correct on these
    * Spectra of rainfall rates (Daily average, not hourly) for all SST experiments with red and white noise significance curves Relaxation type 1:

  • SST = 28
  • SST = 28.5
  • SST = 29
  • SST = 29.5
  • SST = 29.75
  • SST = 30
  • SST = 30.5

    Relaxation type 3:

  • SST = 28
  • SST = 28.5
  • SST = 29
  • SST = 29.5
  • SST = 29.75
  • SST = 30
  • SST = 30.5
    08/24/04

    * Movies of perturbation potential temperature in 2-D model domain relaxation type 3
    Can see waves propagate in the vertical!

    SST = 28.5

  • Hours 1 - 500 (about first 20 days)
  • Hours 1000 - 1441 (final 20 days, day 41 - day 60)

    SST = 29.5

  • Hours 1 - 499 (about first 20 days)
  • Hours 1000 - 1441 (final 20 days, day 41 - day 60)
    08/18/04

    * Movie of Relative Humidity in 2-D model domain with SST = 29.5 relaxation type 3

  • First month
  • Second month
    08/04/04

    * Movie of radiative cooling in 2-D model domain with SST = 29.5 relaxation type 3

    08/03/04

    * Spectrum of the RCE rainfall time series (mean has been removed before FFT applied)
    Relaxation type 1:
    * Spectra of rainfall rates for all SST experiments with red noise significance curve and mean removed:

  • All frequencies shown
    No peaks are significantly different from red noise except: For the range of SST = 29.5 - 30.5, there is a significant peak at the lowest frequency, at about the length of the time series. I think that this is a result of the mean being so different in the later part of the time series from the mean of the initial transient rainfall. So this peak at low frequency is just picking out a trend I think.

    Relaxation type 3:
    * Boxplot of rainrates from all SST experiments with relaxation type 3

    * Relative humidity for all SST cases type 3:

  • Time and horizontal mean vertical profiles
  • Contour plots
  • Initial (day 1), final and time mean vertical profiles

    * Moist static energy for all SST cases type 3:

  • Time and horizontal mean vertical profiles (height)
  • Time and horizontal mean vertical profiles (pressure)
  • Contour plots
  • Initial (day 1), final and time mean vertical profiles

    * Scatterplot of radiative cooling vs. latent heat due to precipitation for all SST cases type 3:

  • Hourly
  • Daily
    If we fit a line to any of the SST experiments (daily mean values) the slope of that line increases as SST increases for SST = 28 the slope is 1.4 and for SST = 30, slope is 5.4. Maximum slope is 6.5 for SST = 30.5.

    * Scatterplot of total tropospheric precipitable water vs. rainrate for all SST cases type 3:

  • Daily (with top of troposphere at 14 km)
  • Daily (with top of troposphere at 16.6 km)
    Nonlinear relationship here as with relaxation type 1 experiments.

    * WTG vertical velocity profiles for all SST cases type 3

    08/02/04

    Relaxation type 1:
    Confidence intervals are not right on these
    * Spectra of rainfall rates for all SST experiments with red noise significance curve

  • All frequencies shown
  • Cut off the "0" frequency
    I think that there is some aliasing. Experimenting with the 90 days of RCE run (the longest run that we have) we can see that a low pass filter eliminates the single significant peak at 0 frequency in the spectrum of the rainfall rate.
    * Spectrum of the 90-day RCE run with significant difference from red noise shown
  • No filter
  • Low-pass filter (5 hour running mean)
  • Low-pass filter (10 hour running mean)
    07/28/04

    * Lag cross-correlation coefficient for rainfall rate and evaporation for last 30 days of runs with relaxation type 1:

  • SST = 28 max rho = 0.82; falls below 0.6 at -8, +8 days
  • SST = 28.5 max rho = 0.84; falls below 0.6 at -8, +9 days
  • SST = 29 max rho = 0.87; falls below 0.6 at -13, +7 days
  • SST = 29.5 max rho = 0.9; falls below 0.6 at -11, +9 days
    07/22/04 - 07/23/04

    Range of the freezing level/height in the model. Height increases with increasing SST.

  • Relaxation type 1: 6.3 - 6.6 km (SST = 28 C -- 31 C)
  • Relaxation type 2: 6.3 - 6.8 km (SST = 28 C -- 30 C)
  • Relaxation type 3: 6.3 - 6.75 km (SST = 27 C -- 30 C)

    Using relaxation type 1 (f = half sine wave)
    * Power Spectral Density of Rainrate with 95% confidence interval
    Frequencies corresponding to a significant peaks in power for each time series are given in 1/day.

  • SST = 28 C
  • SST = 28.5 C
  • SST = 29 C
  • SST = 29.5 C
  • SST = 29.75 C
  • SST = 30 C
  • SST = 30.5 C
  • SST = 31 C
    * Top 20 significant peaks in rainrate PSD plots above
  • Zoom in on lower frequencies
  • Zoom in on mid-frequencies
  • Zoom in on high frequencies

    07/15/04

    Using relaxation type 1 (f= half sine wave)
    I don't believe that the cross-correlation is the right approach to investigate causality between rainrate and evaporation.
    You'll see approximately the same results if I cross-correlate rainrate with evaporation:
    * Cross-correlation of rainrate and evaporation
    as if I cross-correlate rainrate with its own mean:
    * Cross-correlation of rainrate and mean rainrate
    Should think of a better way to do this. How could we study the model evaporation in a different way? Try again with a new measure of evaporation to compare to precip.? Perhaps a spatial and not a temporal approach?

    07/12/04-07/13/04

    Using relaxation type 3 (f=1.0 from top of PBL to top of model)

    SST = 29.5 C

    * Hovmoeller of cloud ice and cloud water in the column

    * Total Precip and Rainrate, 455.5 mm = total rainfall after 60 days

    * Relative humidity contours
    * Relative humidity profiles

    * Mean vertical velocity
    * Vertical velocity contours with hourly rainrate

    * Temperature
    * Potential Temperature
    * Perturbation Potential Temperature

    07/09/04

    Using relaxation type 2 (f=1.0 from top of PBL to tropopause then linear interpolation to top of model)
    * Moist Static Energy

  • Contour plots
  • Mean Vertical Profiles
  • Mean Vertical profiles over lowest 8 km of troposphere
  • Initial, Final and Mean Vertical Profiles

    07/08/04

    Using relaxation type 2 (f=1.0 from top of PBL to tropopause then linear interpolation to top of model)
    * Column Cloud Ice + Cloud Water Hovmoller (longitude vs. time) for final week of experiments.

  • SST = 28
  • SST = 29
  • SST = 29.5
  • SST = 29.75
  • SST = 30
    Discussion:
    All of the cloud contour plots above have comparable colorbars (0 to 4 or 5 mm). So that the maximum amount of cloud in any column (grid point along the horizontal axis) is about the same.
    Clouds in case SST = 30C are much larger in area (look like connected structures with several local maxima) than the clouds in cases with lower SST. Those in the lower SST cases are mostly individual clouds with a single maximum.
    All of the small clouds in the various cases are born and decay over the course of hours it seems.
    All clouds are carried along by the mean easterlies. It seems to take a day or less for a cloud cluster to move across the domain (about 5.9 m/s).

    Using relaxation type 2 (f=1.0 from top of PBL to tropopause then linear interpolation to top of model)

    * Statistics of rainrate and the total precip.
    * Histograms of rainrate
    * Boxplots of rainrate
    Compare with old relaxation type (f=1/2 sin from surface to tropopause)
    * Statistics of rainrate and the total precip.
    * Histograms of rainrate
    * Boxplots of rainrate

    * Relative Humidity varying SST (28, 29, 29.5, 29.75, 30 C) with fixed tau = 2 hrs

  • Contour plots
  • Mean Vertical Profiles
  • Mean Vertical profiles over lowest 8 km of troposphere
  • Initial, Final and Mean Vertical Profiles
    * Relative Humidity with fixed SST = 29.5 and varying relaxation time tau (1, 2, 6 hours)
  • Contour plots
  • Mean Vertical Profiles
  • Mean Vertical profiles over lowest 8 km of troposphere
  • Initial, Final and Mean Vertical Profiles
    06/22/04 --- 07/07/04

    Using Type 2 relaxation (f=1.0 from top of PBL to tropopause then linear interpolation to top of model):

    * Mean vertical profile of Wwtg

  • SST = 28
  • SST = 29
  • SST = 29.5
  • SST = 29.75
  • SST = 30

    * Contour plot of vertical profile over last 30 days of Wwtg vertical profile with rainrates.

  • SST = 28
  • SST = 29
  • SST = 29.5
  • SST = 29.75
  • SST = 30 (last 30 days)
  • SST = 30 (day 20 - day 40)

    Total Precipitation after 60 days with two relaxation schemes
    SST [C] type 1 [mm] type 2 [mm] type 2 / type 1
    28 174.7209.8 1.20
    29 401.6 309.4 0.77
    29.5 710.7 484.6 0.68
    29.75 1258.5 680.7 0.54
    30 1955.6 1547.5 0.79

    For reference: 240.3 mm is the total precip of RCE run after 60 days

    06/11/04
    * Scatterplot of tropospheric precipitable water vs. rainfall rate.
    (All 60 days for all SST cases.) Nonlinear relationship emerges.
  • Hourly
  • Daily
  • Weekly

    06/10/04
    * Scatterplot of radiative cooling vs. LH due to precipitation for all SST cases.
    Linear relationship exists when we consider all the SSTs.

  • Final 30 days
  • All 60 days
  • All 60 days (Hourly)

    06/08/04
    Ratio of Gross Moist Stability to Gross Dry Stability (M/Ms)
    Horizontal red lines at -1.0 and 1.0
    * SST = 28
    * SST = 29
    * SST = 29.75
    * SST = 30

    Gross stability parameters calculated using the 30-day mean vertical profiles of Wwtg and MSE
    SST M Ms M/Ms
    28 -0.68014 -8.2918 0.082025
    29 59.1265 146.6794 0.4031
    29.75 504.9121 1592.3886 0.31708
    30 1081.5632 3021.6909 0.35793

    06/03/04
    Precipitation and Evaporation
    mm/hr
    * Boxplots
    * Medians
    * Means
    mm/day
    * Boxplots
    * Medians
    * Means

    05/18/04
    * Daily values of Radiative Cooling vs. latent heating (Rainrate)
    Slope seems to be about 6. I haven't fit a line yet.

    05/17/04
    Looking at the tropospheric radiative cooling [K day-1] vs rainrate [mm hr-1] and at the same two variables converted to same units W m-2 (rainrate becomes latent heating).
    SST = 30.5 C
  • Hourly
  • Daily
  • Hourly, daily and weekly
  • Hourly, daily and weekly with regression lines
    SST = 29.5 C
  • Hourly
  • Daily
  • Hourly, daily and weekly
  • Hourly, daily and weekly with regression lines

    04/29/04

    Plots of the total potential temperature (PT), PT anomalies and the difference between PT and the target sounding (RCE PT profile). Fields are shown for SST = 28, 29, 29.5 and 29.75.

    In figure 1 (SST < 29.75) the tropopause (which I think might be at the blue-green to green contours) seems stable if not for the last 30 days then perhaps for the last 15 days. And in these cases (SST < 29.75) it seems that the tropopause descends just a little over time. In contrast, when SST = 29.75 just beyond the bifurcation, the tropopause rises during the final days of the run.

    In figure 2a, the anomalous PT shows just how much the model PT is changing in the last 30 days of the 60-day runs. It isn't completely stable; it is still changing +5/-5 degrees Kelvin.

    Figure 2b shows that the model PT relaxes to the target sounding uniformly through the troposphere for all SST shown. We're not relaxing to RCE in the stratosphere (above 15km), but I've measured the difference there anyway. For SST < 29.75, I suppose that we're still close enough to SST = 28 (where we made the RCE estimate) that the stratosphere adjusts to near RCE. As the SST is increased the model stratospheric PT is different from RCE for longer and longer times until at SST = 29.75 the PT is really doing its own thing.

    Set of Figure 1. Potential temperature (totals) vertical profiles:
     * SST = 28
    * SST = 29
    * SST = 29.5
    * SST = 29.75

    Set of Figure 2:
    a) Potential temperature anomalies (top plot)
    b) Difference between potential temperature and RCE (bottom plot)
    * SST = 28
    * SST = 29
    * SST = 29.5
    * SST = 29.75

    04/21/04
    * Daily rainrate vs. tropospheric precipitable water (TPW) [Dashed line is TPW regressed on the rainrate].
    SST = 29C --> time scale 9.7 hours (slope of regressed line)
    I've looked at the Bretherton et. al. paper (J. Climate April 2004) and they estimate a convective timescale of 16 hours for the
    "time scale dW/dP over which the precip. increase dP would remove the excess water vapor dW from the column".
    I am not sure that my graph produces a comparable functional relationship.

    For comparison, the time scales of two other cases (graphs not shown) are
    SST = 28C --> time scale = 60.5 hours (we calculated RCE at 28 C so should we care about this case?)
    SST = 30C --> time scale = 10.3 hours

    * Weekly radiative cooling vs. precip All units W m-2.
    Low SST at the bottom of the plot. Increasing SST as the Dashed line was added by me by hand.
    * Weekly precip vs. radiative cooling All units W m-2.
    Low SST at the left of the plot. Increasing SST as the Dashed line was added by me by hand.

    * Hovmoeller of column cloud ice and cloud water [mm]
    * Hovmoeller of column cloud water [mm]

    04/20/04
    Testing the dependence of the mean on the timeseries -- the particular sequence of 30 days taken out of the 60 day run. We take a number of 30 day ensembles out at random from the 60 days of the RCE run (ext =_01.26.04.RCE)
    * Rainrate
    * Weekly precipitation
    * Monthly precipitation

    No longer allow clipping of wwtg at 6 cm s-1

    UPDATED 04/21/04
    04/09/04 --- 04/12/04
    Varied SST. large domain (NX = 514). with relaxation scheme C.
    Vertical profiles, hourly averages over the last 30 days of a 60 day run.
    * Statistics of rainrate and the total precip.
    * Histograms of rainrate
    * Boxplots of rainrate

    * Relative humidity: Contour plots
    * Relative humidity: vertical profiles

    * Moist Static Energy: Contour plots
    * Moist Static Energy: vertical profiles
    * Moist Static Energy: vertical profiles overlapped
    * Moist Static Energy: vertical profiles overlapped ZOOM!

    * Vertical profiles of W wtg, cloud ice and cloud water:

  • SST = 27.9 C
  • More of these are on the way

    Scatterplots

    * Tropospheric mass weighted radiative cooling vs. rainrate
    * Tropospheric total precipitable water vs. rainrate

    Variable Relaxation throughout the troposphere

    03/18/04
    Varied SST. large domain (NX = 514). with relaxation scheme C.
    Vertical profiles, hourly averages over the last 30 days of a 60 day run.
    At SST = 27, the model is bone dry. The model

    * Moist static energy
    * Relative humidity
    * Statistics of rainrate and the total precip.
    * Histogram of rainrates
    * Boxplots, visual statistics of rainrates

    03/08/04 -- 03/09/04
    Compares 3 relaxation schemes:

  • A. Our relaxation. Constant relaxation throughout the vertical.
  • B. Our relaxation. Variable relaxation throughout the vertical.
  • C. Dave's relaxation scheme. Variable relaxation throughout the vertical.
    * MSE: SST = 29 in all cases. large domain (NX=514).
    * RH: SST = 29 in all cases. large domain (NX=514).

    Varied SST. small domain (NX = 66). with relaxation scheme C.
    Vertical profiles, hourly averages over the last 30 days of a 60 day run.
    * Moist static energy
    * Relative humidity (bump at 5km is freezing level. see next moisture fields below)
    * Precip. and cloud water and ice(freezing level is at about 5km)
    * Contour plots of last 5 days of moisture fields:

    * Wwtg
    * Potential temperature
    * Potential temperature: Zoom in on lowest 5km
    * Radiative cooling
    * Radiative cooling: Zoom in on lowest 15km

    03/01/04
    Defines Relaxation type 1 (f = half sine wave)
    * Weighting function applied to the temperature relaxation term as a function of height not of level k
    * Moist static energy profiles New profile uses the Sine curve which is a function of level and not height.
    The variable relaxation throughout the troposphere shifts where the regime changes take place in SST parameter space. Note that the old curve for SST = 29 (green circles) is in the moderate regime. The new curve (black circles) with relaxation is between the moderate and wet regimes. With variable relaxation, it rains constantly after day 2 and the total precip after 60 days is almost 2 meters of rain. In the previous case for SST=29 C, we get only 0.3 meters of rain after 60 days.

    02/23/04 Summary of long runs with variable SST
    * Relative humidity profiles
    * Total Precip and rain rates with variable SST.
    * Moist Static Energy
    02/09/04
    * Relative humidity profiles with variable SST.
    * Total Precip and rain rates with variable SST.
    * Radiative Cooling.
    * WTG vertical velocity
    * Moist Static Energy

    2/10/04
    SST = 29
    * Time mean vertical profiles (snow, rain, cloud ice, etc.)
    * Moisture Timeseries (averaged over entire domain)
    * Rain, snow, graupel, cloud ice, cloud liquid water
    SST = 30
    * Time mean vertical profiles (snow, rain, cloud ice, etc.)
    * Moisture Timeseries (averaged over entire domain)
    * Rain, snow, graupel, cloud ice, cloud liquid water
    SST = 31
    * Time mean vertical profiles (snow, rain, cloud ice, etc.)
    * Moisture Timeseries (averaged over entire domain)
    * Rain, snow, graupel, cloud ice, cloud liquid water

    WTG run relaxing back to RCE temp. profile (ten days only. not long enough)

    1/29/04
    Total Precip. [mm] and rainfall rates [mm/hr] and [mm/day] after 10 days
    * SST=28
    * SST=29
    * SST=30
    * SST=30.5
    * SST=31
    * SST vs. Precip total and mean rainrate

    RCE run for 90 days with correct solar zenith angle (constant at cosz=0.25)


    1/26/04
    * Total precipitation and Rainfall rates (in mm/hr and mm/day)

    * Radiative cooling vertical profiles at different days during the 90-day run in [K/day]

    * Potential temperature vertical profiles for the 90-day run
    * Temperature vertical profiles for the 90-day run
    * RCE temperature profiles averaged over the last 30 days of the 90-day run

    Searching for Multiple Equilbria. (do they exist?)


    1/6/04 Correct temperature profiles (T and θ)
    * Initial T and θ profiles taken from inside the GCEM (subroutine base)
    * RCE T and θ profiles

    Temp = ƒ (Potential Temp) : T = θ (P0 / P)-0.286

    1/6/04 So far, there is a completely dry state I'm running with a new initial temperature profile defined as the RCE profile + 5 degrees. (10 days; SST = 28.0; Domain is 514 km by 43 levels)
    *

    RCE case run (90 days; SST = 28.0; Domain is 514 km by 43 levels)

    11/19/03
    * RCE Relaxation profile used in WTG scheme
    * 90-day evolution of the mean vertical profile (zonally averaged over the 514 km)
    * 90-day evolution of the mean and anomaly vertical profiles (zonally averaged over the 514 km)

    * The RCE run stabilizes over the last 30 days:

  • time series of d(theta)/dt, where theta is the mean vertical potential temperature and dt = 1 hour
  • time average of the previous figure

    • * Total Precipitation and Rainfall rate

    Testing whether the relaxation profiles are implemented correctly

    11/14/03
    water vapor FIXED
    Run for 30 days with SST=30 about an RCE profile which is found with SST = 28.
    Data taken every hour.
    * RMS Difference between the evolving potential temperature vertical profile and the RCE profile that it is being relaxed to.
  • The differences decrease over time as they should.

    11/12/03
    water vapor NOT FIXED
    Run for 30 days with SST=29 about an RCE profile which is found with SST = 28.
    Data taken every 2 hours.
    * RMS Difference between the evolving potential temperature vertical profile and the RCE profile that it is being relaxed to.

  • The differences decrease over time as they should.

    water vapor FIXED
    Run for 30 days with SST=31 about an RCE profile which is found with SST = 28.
    Data taken every 2 hours.
    * RMS Difference between the evolving potential temperature vertical profile and the RCE profile that it is being relaxed to.

  • Differences decrease after initialization, but begin to increase in the middle of the atmosphere after about 15 days.
  • A longer run with the correct RCE profile (which means one that comes from the integration of the model with Tao's water vapor fix in it).

    Testing the code revised by Tao

    11/12/03
    water vapor FIXED
    Run for 30 days with SST= 31 about an RCE profile which is found with SST = 28.
    Data taken every 2 hours.
    * total water vapor averaged over the 66x43 space domain
  • minima are mostly negative O(10-6)
  • means are positive O(10-3)
    * perturbation water vapor averaged over the 66x43 space domain
  • minima are negative O(10-3)
  • means are O(10-5)
    * mean water vapor profile averaged over the 1x43 space domain
  • minima are mostly positive O(10-7)
  • means are positive O(10-3)

    11/11/03
    water vapor FIXED
    Run for 10 days with SST = 28 about an RCE profile which is found with SST = 28.
    Data taken every 2 hours.
    * total water vapor averaged over the 66x43 space domain

  • minima are negative O(10-6)
  • means are positive O(10-3)
    * perturbation water vapor averaged over the 66x43 space domain
  • minima are negative O(10-3)
  • means are O(10-5)
    * mean water vapor profile averaged over the 1x43 space domain
  • minima can be negative O(10-8)
  • means are positive O(10-3)

    water vapor NOT FIXED
    Results from the model before changes were made to fix negative water vapor.
    Run for 30 days with SST = 29 about an RCE profile which is found with SST = 28.
    Data taken every 2 hours.
    * total water vapor averaged over the 66x43 space domain

  • minima can be negative O(10-2)
  • means are positive O(10-3)
    * perturbation water vapor averaged over the 66x43 space domain
  • minima are negative O(10-2)
  • means are O(10-5)
    * mean water vapor profile averaged over the 1x43 space domain
  • minima can be negative O(10-2)
  • means are positive O(10-3)

    Total Precipitation and Rain rate

    10/22/03
    * SST=28.0
    * SST=28.5
    * SST=29.0
    * SST=29.5
    * SST=30.0
    * Potential temperature vertical profiles (RCE run for 90 days)

    GCEM

    * Code as of Monday, September 8, 2003
    * fakesounding.in
    * params_gridsize.in
    * params_gridsize2.in
    * other pieces of code

    Journal

  • Monday April 28, 2003   
  • Tuesday May 20, 2003    
  • Thursday May 22, 2003    

    CORRECTION: some units have been mislabeled!

  • Dan has said that g/g are the units used for moisture in the model in general and not g/kg
  • rain rate should be in mm/hr not in mm/s
  • wwtg = vertical velocity, should be in cm/s not in m/s
  • tt_r = static stability, is K/cm
  • tt_mf = diabatic heating rate used to calculate wwtg is K/s

    • Radiative-Convective Equlibrium trial run (15 days, SST = 28) with modified inital soundings (nonzero mixing ratio)

    *9/03/03 Average water vapor profile: values in the lower part of the domain are on the order 10-3
    *9/03/03 Average water vapor profile (zoom in on negative values): note that the negative values are on the order 10-5

    Average temperature sounding with corresponding theoretical moisture profiles

    *8/29/03 Average temperature sounding
    *8/29/03
    *8/29/03

    Radiative-Convective Equlibrium trial run (15 days, SST = 28)

    *8/26/03 Total Precip
    *8/26/03 Rainrate
    *8/26/03 Histogram of Rainrate

    *8/26/03 Precipitable water (rain, snow and graupel) over time
    *8/26/03 Average profile of precipitable water (rain, snow and graupel)

    *8/26/03 Cloud water over time
    *8/26/03 Average profile of cloud water

    *8/26/03 Water vapor over time
    *8/26/03 Average profile of water vapor

    Results of using Raymond's method of WTG approximation
    with tau = 1 hour and SST = 31 C

    Up until now, SST = 29.5 C was being used in all of the GCEM runs and we suspected that we were running the model close to Radiative-Convective Equlibrium (29.5 just might happen to be the right value for the model to achieve RCE)

    *7/11/03 Diabatic heating contour plots
    *7/11/03 Diabatic heating mean profiles; at all heights
    *7/11/03 Diabatic heating mean profiles, overlayed; heights between 1 and 10.5 km
    *7/11/03 Diabatic heating mean profiles, overlayed; at all heights

    Mean Diabatic heating averaged over all heights [K/s]: Finally, we are getting a mean on the order of 10-5 !

  • 9.245 x 10-4 : our WTG scheme; 1 minute; SST = 29.5 C
  • 6.700 x 10-6 : our WTG scheme; 1 hour; SST = 29.5 C
  • 9.214 x 10-4 : Raymond WTG scheme; 1 minute; SST = 29.5 C
  • 7.100 x 10-6 : Raymond WTG scheme; 1 hour; SST = 29.5 C
  • 7.180 x 10-5 : Raymond WTG scheme; 1 hour; SST = 31 C
    • Precipitation:
    Lots more precipitation with SST = 31 instead of 29.5
    *7/11/03 Total precipitation : Radically different total precip when SST = 31 C instead of 29.5 C
    *7/11/03 Time series of rainfall rates : Radically different total precip when SST = 31 C instead of 29.5 C
    *7/11/03 Histogram of rainfall rates
    Mean/Variance of Rainrate [mm/hr]/[mm2/hr2]
  • 0.1428/0.0455 : our WTG scheme; 1 minute; SST = 29.5 C
  • 0.1387/0.0226 : our WTG scheme; 1 hour; SST = 29.5 C
  • 0.1137/0.0233 : Raymond WTG scheme; 1 minute; SST = 29.5 C
  • 0.1316/0.0260 : Raymond WTG scheme; 1 hour; SST = 29.5 C
  • 1.3253/0.6221 : Raymond WTG scheme; 1 hour; SST = 31 C

    • Total Precipitation at end of 9 days

  • 30.8547 mm : our WTG scheme; 1 minute; SST = 29.5 C
  • 29.9510 mm: our WTG scheme; 1 hour; SST = 29.5 C
  • 24.5562 mm: Raymond WTG scheme; 1 minute; SST = 29.5 C
  • 28.4188 mm : Raymond WTG scheme; 1 hour; SST = 29.5 C
  • 286.2604 mm : Raymond WTG scheme; 1 hour; SST = 31 C

    • Vertical Velocity [cm/s]:
    Stronger vertical wind (up to 5 cm/s) accompanies the increase in precipitation
    *7/11/03 9-day mean vertical velocity at all heights.
    *7/11/03 9-days of vertical velocity time vs. height

    Tempreature [K]:
    *7/11/03 Potential temperature
    *7/11/03 Mean potential temperature

    Moisture [g/g] :
    Cloud water profile is enhanced. More cloud water to precipitate out
    *7/11/03 9-day mean Cloud water
    *7/11/03 9-days of Cloud water , time vs. height

    From 4 to 8 times more precipitable water when SST = 31 C than when we set SST = 29.5
    *7/11/03 9-day mean Precipitable water
    *7/11/03 9-days Precipitable water , time vs. height

    More water vapor between the surface and 10km than in the cases where SST = 29.5
    *7/11/03 9-day mean water vapor
    *7/11/03 9-days water vapor , time vs. height

    Comparision of our WTG and Raymond's method of WTG approximation with two relaxation times, tau, for each: 1 minute and 1 hour.
    (all runs are 9 days long and SST = 29.5 C)

    Two schemes for the total heating uesd in WTG (tt_m):
    Ours: tt_m = tt_m + (TT_F_B - TT_F_O)/tau
    Raymond's: tt_m = (TT_F_B - TT_F_O)/tau

    Vertical Velocity [cm/s]:
    *7/08/03 9-day mean vertical velocity at all heights.
    The magenta line seems smoothest to my eye overall; that line is made using Dave Raymond's scheme and tau = 1hour.
    *7/08/03 9-day mean vertical velocity from surface to 10.5 km
    *7/08/03 9-day mean vertical velocity above boundary layer to 10.5 km
    *7/08/03 9-days of vertical velocity , time vs. height
    This graphic and the next one support my idea that the Raymond scheme with tau = 1 hour (bottom panel) is the smoothest overall. Also note the colorbars: the bottom panel has the smallest negative values of all the other cases and the darkest red here is greater than 4 cm/s unlike the others.
    *7/08/03 3-days vertical velocity , time vs. height

    Moisture [g/g] :
    *7/08/03 9-day mean Cloud water
    *7/08/03 9-days of Cloud water , time vs. height
    *7/08/03 3-days of Cloud water , time vs. height

    *7/08/03 9-day mean Precipitable water
    *7/08/03 9-days Precipitable water , time vs. height
    *7/08/03 3-days Precipitable water , time vs. height

    *7/08/03 9-day mean Water vapor
    Recall that the two runs made with tau = 1 hour (our WTG) and tau = 1 minute (Raymond WTG) show negative values around 9-12 km up. We no longer have that with SST = 31, except for a single negative value at the very top of the model, which doesn't concern me much as it is right at the top boundary.
    *7/08/03 9-day mean Water vapor zoomed in
    In the time mean, two of these water vapor profiles show negative values around 9-12 km up. These are the runs that are made with tau = 1 hour (our WTG) and tau = 1 minute (Raymond WTG). The next graphic shows snapshots in time of thes four different water vapor profiles.
    *7/08/03 Water vapor profile snapshots in the center of the column on different days
    Notice that around days 4 and 5 some of the profiles become negative. By day 8, all of the profiles have some negative values. However, the case using our WTG and tau = 1 minute has the smallest excursion into negative values.
    *7/08/03 9-days Water vapor , time vs. height
    *7/08/03 3-days Water vapor , time vs. height

    Precipitation:
    *7/03/03 Total precipitation
    *7/03/03 Time series of rainfall rates
    *7/03/03 Histogram of rainfall rates

    Mean/Variance of Rainrate [mm/hr]/[mm2/hr2]

  • 0.1428/0.0455 : our WTG scheme; 1 minute
  • 0.1387/0.0226 : our WTG scheme; 1 hour
  • 0.1137/0.0233 : Raymond WTG scheme; 1 minute
  • 0.1316/0.0260 : Raymond WTG scheme; 1 hour

    • Total Precipitation at end of 9 days

  • 30.8547 mm : our WTG scheme; 1 minute
  • 29.9510 mm: our WTG scheme; 1 hour
  • 24.5562 mm: Raymond WTG scheme; 1 minute
  • 28.4188 mm : Raymond WTG scheme; 1 hour
    • Diabatic heating [K/s]:
    *7/03/03 Diabatic heating contour plots:
    Both schemes with tau = 1 hour yield more uniform values of the heating throughout the height of the model. Notice the values on the colorbar. It is more obvious in the following plots of the mean...
    *7/03/03 Mean diabatic heating at all heights
    Plots a and c (made with tau = 1 minute) regardless of WTG scheme, seem to have straightline profiles away from the boundary layers. This is merely because of the O(102) increase in the values at top and bottom of the domain in these two cases. The next plot shows that all four runs have a similar mean profile in the middle.
    *7/03/03 Mean diabatic heating above PBL up to about 10.5 km
    These four profiles are time averaged. If I average them over these heights that are shown (1 km - 10.5 km) the average values are
  • -1.649 x 10-5 K/s : our WTG scheme; 1 minute
  • -6.510 x 10-6 K/s : our WTG scheme; 1 hour
  • -1.786 x 10-5 K/s : Raymond WTG scheme; 1 minute
  • -1.805 x 10-5 K/s : Raymond WTG scheme; 1 hour

    • Static Stability [K/cm]:
    *7/03/03 Static stability profiles for the four different runs. They are striking in their similarity.
    *7/03/03 Static stability profiles from previous graph, but now they are overplotted to see the close fit between them all.
    *7/03/03 Static stability as a time vs. height contour plot.

    Tempreature [K]:
    *7/03/03 Potential temperature
    *7/03/03 Mean potential temperature
    These four profiles are time averaged. And if I take a vertical average they are essentially the the same:

  • 346.8552 K : our WTG scheme; 1 minute
  • 346.7911 K : our WTG scheme; 1 hour
  • 346.8933 K : Raymond WTG scheme; 1 minute
  • 346.8450 K : Raymond WTG scheme; 1 hour

    • Diabatic heating: with a relaxation time of one minute (tau = 1.*60.)

  • In this case we were seeing rather large negative values of the heating in the PBL and large positive ones at the top of the model.
  • In the next case (below) we do not see this!

    *6/30/03 Diabatic heating profiles at 10 different times (tt_mf) is used to calculate wwtg
    The top panel is the heating at all heights. The bottom shows only the heights between about 1 and 10.5 km. This is to show that the large variations (on the order of 10-2) are in the stratosphere or in the boundary layer only. In between, the variations are on the order of 10-4.
    *6/26/03 Diabatic heating (tt_mf) used to calculate wwtg

    Diabatic heating: with a relaxation time of one hour (tau = (60.*60.)

  • Unlike the case above with the shorter relaxation time, here the max and min values of heating are on the order of 10-4 EVERYWHERE.

    *7/01/03 Diabatic heating profiles at 10 different times (tt_mf) is used to calculate wwtg
    The top panel is the heating at all heights. The bottom shows only the heights between about 1 and 10.5 km. In contrast to the 1 minute relaxation time case, the variations here are all on the order of 10-4!
    *7/01/03 Diabatic heating (tt_mf) used to calculate wwtg
    *7/01/03 Deviation of the mean heating profile (ta) from its own mean (with respect to time) at several different model levels for a 9-day run.
    We are no longer implementing Guojun's modification to ta. The following lines were commented out:
    do k=9,NZ-1
    ta(k)=ta(k)-(TT_F_B(k)-TT_F_O(k))*12./(1.*60.)
    enddo
    ??By definition I thought that the "mean heating profile" was not supposed to change??
    Could this be why Guojun was relaxing "ta" the mean temperature profile?
    Profiles at level 40-43 are the ones with the largest changes from the mean over time.
    These profiles have variance: 0.5094, 1.4902, 3.7987, 7.1891, respectively.
    Most of the levels below these vary 10^-2 .

    Compare precip. over two different relaxation times

    *7/01/03 Total precip
    *7/01/03 Rainrate over 9-days

    Precipitation Statistics
    relaxation times -----> 1 minute 1 hour
    time-mean rainrate [mm/hr] 0.1428 0.1387
    total precip [mm] 30.8547 29.9510

    Relaxation temperature profiles

    *6/26/03 Time mean of the relaxation profiles TT_F_O, TT_F, TT_F_B that are used to calculate diabatic heating (tt_mf)
    *6/26/03 Relaxation term: (TT_F_B - TT_F_O) /60
    After nine days there is a noticeable oscillation at the tropopause.
    *6/26/03 Relaxation term if we were to use TT_F: (TT_F - TT_F_O) /60
    After nine days there is still a noticeable oscillation above the tropopause.

    *6/26/03 Total precipitation with (Guojun's) and without (ours) a modified pot. temp. profile "ta" for a nine day run
    Guojun's total precip: 28.4988 mm
    Our total precip: 30.8547 mm

    horizontal average of dpt

    *6/26/03 A mean taken over all 9-days of the horizontal average of "dpt"
    dpt = perturbation potential temperature
    NOTE: x-axis is multiplied by 10-4
    *6/26/03 Horizontal average of "dpt" shown every 20 minutes over 9 days
    NOTE: colorbar is multiplied by 10-3
    *6/26/03 Horizontal average of "dpt" zoomed in on the graph above
    NOTE: colorbar is multiplied by 10-3

    Effects of smoothing static stability with 1-2-1 filter

    Results below are from two 9-day integrations exactly the same parameters, except with and without smoothed static stability profiles.


    Static stability:
    * Static stability profiles used in the two integrations (smoothed and unsmoothed):
    The kink in the unsmoothed profile (blue dashed line) is eliminated with smoothing (solid red line). (From the top left panel, moving clockwise the profiles are taken from the beginning of days: 4, 5, 9, 7.)
    * Static stability profiles at same time as above, but for 15 km and below:
    this shows the details which are lost in the previous set of profiles. The smoothing is much more apparent here.
    * Average static stability profiles over the last 5-days of the 9-day run :
    this does not look very different from the snapshot profiles above.
    * Average static stability profiles same as above, but for 15 km and below:
    again, not much difference in the average from the snapshot profiles.

    Precip and rain rate:
    * total precipitation:
    after 25 hours the precip begins to differ
    * rainrates:
    after 19 hours the rates begin to differ

    Vertical velocity:
    * vertical velocity profiles at 4 different times:
    when the static stability is not smoothed (dashed line) the profiles are much spikier. A smoother static stability (red, solid line) results in a w-profile with much smaller vertical gradient (d/dz). The x-axis is mislabeled "average w", but it is really the w at a particular point in time. From the top left panel, moving clockwise the profiles are taken from the beginning of day: 4, 5, 9, 7.

    * Average vertical velocity profiles over the last 5-days of the 9-day run :
    on average the vertical velocity without smoothing is reduced at all heights, but it is still rather spiky especially above 10 km.

    The following two pictures do not illustrate the changes in vertical velocity as well as the four-panel picture above.
    * vertical velocity every 20 minutes
    * vertical velocity every 60 minutes

    Rain, snow and graupel:
    * Rain, snow and graupel every 20 minutes:
    the hydrometeors are confined to below 15 km with smoothing of the static stability profile and without it. The scale on the right shows that the maximum concentration doesn't change much between the two cases, just by 0.01. The timing of precipitation events is different in the two cases as we'd expect, knowing that the rain rates differ significantly.
    * Rain, snow and graupel as above but for lowest 15km

    Rainrate and Precipitation: testing the solar zenith angle

    * 10-day run:
    rainfall total and rain rate (using noon value for insolation cosz = 0.9582)

    * 12-day run:
    rainfall total and rain rate (using average daily value for insolation cosz = 0.7534)

    * comparison of total precipitation for 12 and 10 day runs

    * comparison of rainrates for 12 and 10 day runs

    * comparison of total precipitation for 12 and 11 day runs :
    can zoom in on this

    * comparison of rainrates for 12 and 11 day runs

    Precipitation Statistics
    10-day 11-day12-day
    time-mean rainrate0.1562 0.15690.1657
    time-mean precip13.6734 16.289918.6893
    time-mean precip/total#days1.3673 1.55741.4809

    Clouds and rain:

    The following graphs all begin at day 5 and plot the next 6 days

    * Cloud water and cloud ice: 20 minute resolution

    water no longer seems confined to 20km;
    distinct blobs at 12 and 6 km;
    * Cloud water and cloud ice: 60 minute resolution
    again, there are distinct blobs at 12 and 6 km

    * Rain, snow and graupel: 20 minute resolution

    Now the maxima are at around 6km, but the contours stretch down to the surface
    * Rain, snow and graupel: 60 minute resolution
    Notice the particularly strong precip at about day 10

    Vertical wind: contours in time-height plot

    The last 24 hours of the 12-day run. Exact same wind data is plotted every 5, 20 and 60 minutes.
    * 5 minute resolution
    * 20 minute resolution
    * 60 minute resolution

    Hourly vertical moisture and wind (vertical component) profiles:

    the last 24 hours of a 10 day run
    zonal extent: NX = 514
    cosz = 0.9582

    * qr = precipitable water
    * qc = cloud water
    * qv = water vapor : This profile doesn't seem to change at all. See the average profile over the 10 days below.
    * w = vertical wind

    For comparison with the 10-day run:
    10th day of the 12-day run
    zonal extent NX = 514.
    cosz = 0.7534

    * qr = precipitable water
    * qc = cloud water
    * qv = water vapor
    * w = vertical wind

    Last 24 hours of the 12-day run
    zonal extent NX = 514.
    cosz = 0.7534

    * qr = precipitable water
    * qc = cloud water
    * qv = water vapor
    * w = vertical wind

    Average profiles for the 10 day run:

    * qr = precipitable water
    * qc = cloud water
    * qv = water vapor
    * w = vertical wind

    Average profiles for the 12 day run:

    * qr = precipitable water
    * qc = cloud water
    * qv = water vapor
    * w = vertical wind