diff --git a/_sources/cice_1_introduction.rst.txt b/_sources/cice_1_introduction.rst.txt index 1be56648a..67d6a9ba7 100644 --- a/_sources/cice_1_introduction.rst.txt +++ b/_sources/cice_1_introduction.rst.txt @@ -1,3 +1,5 @@ +:tocdepth: 3 + Introduction - CICE5 ============================================ diff --git a/_sources/cice_2_science_guide.rst.txt b/_sources/cice_2_science_guide.rst.txt index 5fb222326..86efea57d 100644 --- a/_sources/cice_2_science_guide.rst.txt +++ b/_sources/cice_2_science_guide.rst.txt @@ -1,3 +1,5 @@ +:tocdepth: 3 + Science Guide ================ @@ -199,9 +201,10 @@ stable and unstable atmosphere–ice boundary layers. Define the “stability” .. math:: - \Upsilon = {\kappa g z_\circ\over u^{*2}} - \left({\Theta^*\over\Theta_a\left(1+0.606Q_a\right)} + - {Q^*\over 1/0.606 + Q_a}\right), + \Upsilon = {\frac{\kappa g z_\circ}{u^{*2}}} + \left({\frac{\Theta^*}{\Theta_a\left(1+0.606Q_a\right)}} + + {\frac{Q^*}{{1/0.606} + Q_a}}\right), + :label: upsilon where :math:`\kappa` is the von Karman constant, :math:`g` is gravitational acceleration, and :math:`u^*`, :math:`\Theta^*` and @@ -225,7 +228,8 @@ Neglecting form drag,the exchange coefficients :math:`c_u`, :math:`c_\theta` and :math:`c_q` are initialized as .. math:: - \kappa\over \ln(z_{ref}/z_{ice}) + \frac{\kappa}{\ln(z_{ref}/z_{ice}}) + :label: coeffinit and updated during a short iteration, as they depend upon the turbulent scales. The number of iterations is set by the namelist variable @@ -242,8 +246,9 @@ unstable (:math:`\Upsilon <0`) case are given by \begin{aligned} \psi_m = &\mbox{}&2\ln\left[0.5(1+\chi)\right] + \ln\left[0.5(1+\chi^2)\right] -2\tan^{-1}\chi + - {\pi\over 2}, \\ + {\frac{\pi}{2}}, \\ \psi_s = &\mbox{}&2\ln\left[0.5(1+\chi^2)\right].\end{aligned} + :label: psi1 In a departure from the parameterization used in :cite:`KL02`, we use profiles for the stable case @@ -252,14 +257,16 @@ following :cite:`JAM99`, .. math:: \psi_m = \psi_s = -\left[0.7\Upsilon + 0.75\left(\Upsilon-14.3\right) \exp\left(-0.35\Upsilon\right) + 10.7\right]. + :label: psi2 The coefficients are then updated as .. math:: \begin{aligned} - c_u^\prime&=&{c_u\over 1+c_u\left(\lambda-\psi_m\right)/\kappa} \\ - c_\theta^\prime&=& {c_\theta\over 1+c_\theta\left(\lambda-\psi_s\right)/\kappa}\\ + c_u^\prime&=&{\frac{c_u}{1+c_u\left(\lambda-\psi_m\right)/\kappa}} \\ + c_\theta^\prime&=& {\frac{c_\theta}{1+c_\theta\left(\lambda-\psi_s\right)/\kappa}}\\ c_q^\prime&=&c_\theta^\prime\end{aligned} + :label: coeff2 where :math:`\lambda = \ln\left(z_\circ/z_{ref}\right)`. The first iteration ends with new turbulent scales from @@ -268,10 +275,11 @@ heat flux coefficients are computed, along with the wind stress: .. math:: \begin{aligned} - \nonumber C_l&=&\rho_a \left(L_{vap}+L_{ice}\right) u^* c_q \\ C_s&=&\rho_a c_p u^* c_\theta^* + 1, \\ - \vec{\tau}_a&=&{\rho_a u^{*2}\vec{U}_a\over |\vec{U}_a|},\end{aligned} + \vec{\tau}_a&=&{\rho_a \frac{u^{*2}\vec{U}_a}{|\vec{U}_a|}},\end{aligned} + :label: coeff3 + where :math:`L_{vap}` and :math:`L_{ice}` are latent heats of vaporization and fusion, :math:`\rho_a` is the density @@ -299,6 +307,7 @@ computed as .. math:: F_{lw\downarrow} = \epsilon\sigma T_s^4 - \epsilon\sigma T_a^4(0.39-0.05e_a^{1/2})(1-0.8f_{cld}) - 4\epsilon\sigma T_a^3(T_s-T_a) + :label: lwflux where the atmospheric vapor pressure (mb) is :math:`e_a = 1000 Q_a/(0.622+0.378Q_a)`, :math:`\epsilon=0.97` is the @@ -313,6 +322,7 @@ available in function *longwave\_parkinson\_washington*: .. math:: F_{lw\downarrow} = \epsilon\sigma T_a^4 (1-0.261 \exp\left(-7.77\times 10^{-4}T_a^2\right)\left(1 + 0.275f_{cld}\right) + :label: lwflux2 The value of :math:`F_{lw\uparrow}` is different for each ice thickness category, while :math:`F_{lw\downarrow}` depends on the mean value of @@ -324,7 +334,8 @@ incorporates the cloud fraction and humidity through the atmospheric vapor pressure: .. math:: - F_{sw\downarrow} = {1353 \cos^2 Z \over {10^{-3}(\cos Z+2.7)e_a + 1.085\cos Z + 0.1}}\left(1-0.6 f_{cld}^3\right) > 0 + F_{sw\downarrow} = {\frac{1353 \cos^2 Z}{10^{-3}(\cos Z+2.7)e_a + 1.085\cos Z + 0.1}}\left(1-0.6 f_{cld}^3\right) > 0 + :label: swflux where :math:`\cos Z` is the cosine of the solar zenith angle. @@ -395,6 +406,7 @@ to the ice, \begin{aligned} \vec{\tau}_w&=&c_w\rho_w\left|{\vec{U}_w-\vec{u}}\right|\left[\left(\vec{U}_w-\vec{u}\right)\cos\theta +\hat{k}\times\left(\vec{U}_w-\vec{u}\right)\sin\theta\right] \end{aligned} + :label: tauw is then passed to the flux coupler (relative to the ocean) for use by the ocean model. Here, :math:`\theta` is the turning angle between @@ -733,7 +745,7 @@ ice volume :math:`v_{in}`, and snow volume :math:`v_{sn}` for each thickness category :math:`n` are .. math:: - {\partial\over\partial t} (a_{in}) + \nabla \cdot (a_{in} {\bf u}) = 0, + {\frac{\partial}{\partial t}} (a_{in}) + \nabla \cdot (a_{in} {\bf u}) = 0, :label: transport-ai .. math:: @@ -804,11 +816,11 @@ equations for pond area fraction :math:`a_{pnd}a_i` and pond volume :math:`h_{pnd}a_{pnd}a_i`, given the ice velocity :math:`\bf u`, are .. math:: - {\partial\over\partial t} (a_{pnd}a_{i}) + \nabla \cdot (a_{pnd}a_{i} {\bf u}) = 0, + {\frac{\partial}{\partial t}} (a_{pnd}a_{i}) + \nabla \cdot (a_{pnd}a_{i} {\bf u}) = 0, :label: transport-apnd .. math:: - {\partial\over\partial t} (h_{pnd}a_{pnd}a_{i}) + \nabla \cdot (h_{pnd}a_{pnd}a_{i} {\bf u}) = 0. + {\frac{\partial}{\partial t}} (h_{pnd}a_{pnd}a_{i}) + \nabla \cdot (h_{pnd}a_{pnd}a_{i} {\bf u}) = 0. :label: transport-hpnd (These equations represent quantities within one thickness category; @@ -861,6 +873,7 @@ tracer-on-tracer dependencies such as :math:`h_{pnd}`, when needed: .. math:: h_{pnd}^{t+\Delta t}= {h_{pnd}^{t}a_{pnd}^{t}a_{i}^{t} \over a_{pnd}^{t+\Delta t}a_{i}^{t+\Delta t} }. + :label: hpnd In this case (adding new ice), :math:`h_{pnd}` does not change because :math:`a_{pnd}^{t+\Delta t}a_{i}^{t+\Delta t} = a_{pnd}^{t}a_{i}^{t}`. @@ -870,14 +883,15 @@ the total pond area summed over categories :math:`n`, .. math:: \sum_n a_{pnd}^{t+\Delta t}(n)a_{i}^{t+\Delta t}(n) = \sum_n a_{pnd}^{t}(n)a_{i}^{t}(n). + :label: apnd2 Thus, .. math:: \begin{aligned} - \label{eq:xfer} - a_{pnd}^{t+\Delta t}(m)&=& {\sum_n a_{pnd}^{t}(n)a_{i}^{t}(n) - \sum_{n\ne m} a_{pnd}^{t+\Delta t}(n)a_{i}^{t+\Delta t}(n) \over a_i^{t+\Delta t}(m) } \\ - = {a_{pnd}^t(m)a_i^t(m) + \sum_{n\ne m} \Delta \left(a_{pnd}a_i\right)^{t+\Delta t} \over a_i^{t+\Delta t}(m) }\end{aligned} + a_{pnd}^{t+\Delta t}(m) &=& {\sum_n a_{pnd}^{t}(n)a_{i}^{t}(n) - \sum_{n\ne m} a_{pnd}^{t+\Delta t}(n)a_{i}^{t+\Delta t}(n) \over a_i^{t+\Delta t}(m) } \\ + &=& {a_{pnd}^t(m)a_i^t(m) + \sum_{n\ne m} \Delta \left(a_{pnd}a_i\right)^{t+\Delta t} \over a_i^{t+\Delta t}(m) }\end{aligned} + :label: xfer This is more complicated because of the :math:`\Delta` term on the right-hand side, which is handled manually in **ice\_itd.F90**. Such @@ -1063,6 +1077,7 @@ the form .. math:: \frac{d T_b}{dt} = w_b \frac{\Delta T_b}{\Delta z} + R_b({T_j : j = 1,\ldots,N_b}) + :label: tracer1 where :math:`R_b` represents the nonlinear biochemical reaction terms detailed in :cite:`EDHHJJLS12` and :math:`\Delta z` is a @@ -3030,7 +3045,7 @@ the ridge potential energy is modified: .. math:: P = C_f \, C_p \, \beta \sum_{n=1}^{N_C} \left[ -a_{Pn} \, h_n^2 + \frac{a_{Pn}}{k_n} - \left( H_{\min}^2 + 2H_{\min}\lambda + 2 \lambda^2 \right) \right] % CHECK BRACES + \left( H_{\min}^2 + 2H_{\min}\lambda + 2 \lambda^2 \right) \right] :label: roth-strength1 The energy-based ice strength given by Equations :eq:`roth-strength0` or @@ -4293,7 +4308,7 @@ to the temperature, :math:`T`, and the brine volume, :math:`\phi`, by \begin{aligned} q =& \phi q_{br} &+\, (1-\phi) q_{i} =& \phi \rho_{w} c_{w} T &+\, (1-\phi) (\rho_i c_i T - \rho_i L_0) - \label{enthalpy_definition}\end{aligned} + \end{aligned} :label: enth-def where :math:`q_{br}` is the brine enthalpy, :math:`q_i` is the pure ice diff --git a/_sources/cice_3_user_guide.rst.txt b/_sources/cice_3_user_guide.rst.txt index 1c074a515..81e867c03 100644 --- a/_sources/cice_3_user_guide.rst.txt +++ b/_sources/cice_3_user_guide.rst.txt @@ -1,3 +1,5 @@ +:tocdepth: 3 + User Guide ========== @@ -2045,153 +2047,259 @@ Additional Details end of the case directory. For example, "./create.case -m wolf -t smoke -testid t12 -p 4x1" creates the directory wolf_smoke_gx3_4x1.t12. This flag is REQUIRED if using -t or -ts. +.. _compliance: + ~~~~~~~~~~~~~~~~~~~~ -Code compliance test +Code Compliance Test ~~~~~~~~~~~~~~~~~~~~ -Additions and changes to CICE and Icepack are expected to be bit-for-bit -unless there is a strong justification for non-reproducibility, such as -a bug-fix or approved scientific alteration to existing code. However, -situations do arise when additions to CICE or Icepack are not -bit-for-bit, but are also not expected to change the science of CICE and -Icepack. In that instant, further evidence is required in the initial -testing phase to support the premise that code changes have not altered -the science of the model. To support this testing, a :math:`t`-test is -being/has been implemented in the CICE testing infrastructure. - -****** -Method -****** - -Welch’s two-sided :math:`t`-test is used to help determine whether or -not two different simulations that should be identical are significantly -different for any grid cell of the CICE gx-1/3 domain for grid-cell -averaged sea ice thickness, :math:`h`, ice concentration, :math:`c`, and -pack velocity components :math:`\pmb{u}=\pmb{u}(u,v)`. In this -circumstance, we seek to determine whether or not the null hypothesis, -:math:`H_0`, is true. The null hypothesis is: Two simulations that are -not bit-for-bit identical are ostensibly the same at every model grid -point. The test begins from the standpoint that two CICE simulations -*should* be bit-for-bit but are suspected of only being different at the -level of computational innaccuracy. Therefore, we seek to limit a -:math:`t`-test Type II error, where a test would erroneously confirm the -null hypothesis, :math:`H_0`. To that end, we choose to test the -hypothesis that grid-point means from CICE simulation ‘:math:`a`’ are -different from CICE simulation ‘:math:`b`’ at a relatively low -confidence interval. Formally, we test the hypothesis -:math:`H_0:\bar{x}_a=\bar{x}_b`, :math:`H_1:\bar{x}_a\neq\bar{x}_b` for -each of the aforementioned variables at every model grid point using a -two-sided t-test with a 68, 80 and 95% confidence interval. Here, -:math:`\bar{x}{=}\tfrac{1}{n}\sum_{i=1}^n x_i` is the time series mean -of :math:`n` samples :math:`x_i` representing :math:`h`, :math:`c`, -:math:`u` or :math:`v`, and daily samples are used from 5-year -stand-alone CICE simulations. More frequent output is unnecessary, -because each of :math:`h`, :math:`c`, :math:`u` and :math:`v` typically -have a high degree of auto-correlation in sea ice models. - -Due to the strong auto-correlation in geo-located sea ice time series, -we calculate a two-sided :math:`t`-statistic to compare -:math:`\bar{x}_a` and :math:`\bar{x}_b`, given their respective standard -deviations, :math:`\sigma_a` and :math:`\sigma_b`, and effective sample -sizes, :math:`n'_a` and :math:`n'_b`, following -:cite:`vSZ99` : +A core tenet of CICE dycore and Icepack innovations is that they must not change +the physics and biogeochemistry of existing model configurations, notwithstanding +obsolete model components. Therefore, alterations to existing CICE Consortium code +must only fix demonstrable numerical or scientific inaccuracies or bugs, or be +necessary to introduce new science into the code. New physics and biogeochemistry +introduced into the model must not change model answers when switched off, and in +that case CICEcore and Icepack must reproduce answers bit-for-bit as compared to +previous simulations with the same namelist configurations. This bit-for-bit +requirement is common in Earth System Modeling projects, but often cannot be achieved +in practice because model additions may require changes to existing code. In this +circumstance, bit-for-bit reproducibility using one compiler may not be unachievable +on a different computing platform with a different compiler. Therefore, tools for +scientific testing of CICE code changes have been developed to accompany bit-for-bit +testing. These tools exploit the statistical properties of simulated sea ice thickness +to confirm or deny the null hypothesis, which is that new additions to the CICE dycore +and Icepack have not significantly altered simulated ice volume using previous model +configurations. Here we describe the CICE testing tools, which are applies to output +from five-year gx-1 simulations that use the standard CICE atmospheric forcing. +A scientific justification of the testing is provided in +:cite:`Hunke2018`. + +.. _paired: + +******************************* +Two-Stage Paired Thickness Test +******************************* + +The first quality check aims to confirm the null hypotheses +:math:`H_0\!:\!\mu_d{=}0` at every model grid point, given the mean +thickness difference :math:`\mu_d` between paired CICE simulations +‘:math:`a`’ and ‘:math:`b`’ that should be identical. :math:`\mu_d` is +approximated as +:math:`\bar{h}_{d}=\tfrac{1}{n}\sum_{i=1}^n (h_{ai}{-}h_{bi})` for +:math:`n` paired samples of ice thickness :math:`h_{ai}` and +:math:`h_{bi}` in each grid cell of the gx-1 mesh. Following +:cite:`Wilks2006`, the associated :math:`t`-statistic +expects a zero mean, and is therefore .. math:: - t=\frac{\bar{x}_a - \bar{x}_b}{\sqrt{\frac{\sigma^2_a}{n'_a}+\frac{\sigma^2_b}{n'_b}}}. + t=\frac{\bar{h}_{d}}{\sigma_d/\sqrt{n_{eff}}} :label: t-distribution -The null hypothesis :math:`H_0:\bar{x}_a=\bar{x}_b` is true when +given variance +:math:`\sigma_d^{\;2}=\frac{1}{n-1}\sum_{i=1}^{n}(h_{di}-\bar{h}_d)^2` +of :math:`h_{di}{=}(h_{ai}{-}h_{bi})` and effective sample size .. math:: - -t_{crit}({1{-}\alpha/2},N)0.99` is +possible in parts of the gx-1 domain for the five-year QC simulations. +In the event that :math:`H_0` is confirmed but :math:`2\leq n_{eff}<30`, +the :math:`t`-test progresses to the ‘Table Lookup Test’ of +:cite:`Zwiers1995`, to check that the first-stage test +using (:eq:`t-distribution`) was not +conservative. The Table Lookup Test chooses critical :math:`t` values +:math:`|t| - - 1. Introduction - CICE5 — CICE-Consortium 0.0.1 documentation - - - + - + \ No newline at end of file diff --git a/cice_2_science_guide.html b/cice_2_science_guide.html index f79dbae81..755cd4877 100644 --- a/cice_2_science_guide.html +++ b/cice_2_science_guide.html @@ -1,16 +1,13 @@ + - - 2. Science Guide — CICE-Consortium 0.0.1 documentation - - - + - +
@@ -857,7 +854,7 @@

3.1.6.2. Diagnostic filesTimers are declared and initialized in ice_timers.F90, and the code to be timed is wrapped with calls to ice_timer_start and ice_timer_stop. Finally, ice_timer_print writes the results to -the log file. The optional “stats” argument (true/false) prints +the log file. The optional “stats” argument (true/false) prints additional statistics. Calling ice_timer_print_all prints all of the timings at once, rather than having to call each individually. Currently, the timers are set up as in Table 5. @@ -869,8 +866,8 @@

3.1.6.2. Diagnostic filesThe timers use MPI_WTIME for parallel runs and the F90 intrinsic system_clock for single-processor runs.

Table 5 : CICE timers

- - +
Table 5
+@@ -978,7 +975,7 @@

3.1.6.3. Restart filesSHRDIR is a path to the CESM shared code.

Table 6 : Configuration options available in comp_ice.

-

Table 5
- +
Table 6
+@@ -1223,7 +1220,7 @@

3.2.4. Forcing data +
_images/distrb.png

Figure 9

@@ -1263,7 +1260,7 @@

3.2.4. Forcing dataFigure 10 provides an overview of the pros and cons for the distribution types.

-

Table 6
- +
Table 7
+@@ -1867,7 +1864,7 @@

3.6.4.3. To run a test suite to generate baseline datacd base_suite.t02

# Once all jobs finish, concatenate all output

./results.csh # All tests results will be stored in results.log

-

# To plot a timeseries of “total ice extent”, “total ice area”, and “total ice volume”

+

# To plot a timeseries of “total ice extent”, “total ice area”, and “total ice volume”

./timeseries.csh <directory>

ls *.png

@@ -1877,7 +1874,7 @@

3.6.4.4. To run a test suite to compare to baseline data
  • In general, the baseline generation, baseline compare, and test diff are independent.
  • -
    Use the ‘-bd’ flag to specify the location where you want the baseline dataset
    -
    to be written. Without specifying ‘-bd’, the baseline dataset will be written +
    Use the ‘-bd’ flag to specify the location where you want the baseline dataset
    +
    to be written. Without specifying ‘-bd’, the baseline dataset will be written to the default baseline directory found in the env.<machine> file (ICE_MACHINE_BASELINE).
  • -
    If ‘-bd’ is not passed, the scripts will look for baseline datasets in the default
    +
    If ‘-bd’ is not passed, the scripts will look for baseline datasets in the default
    baseline directory found in the env.<machine> file (ICE_MACHINE_BASELINE). -If the ‘-bd’ option is passed, the scripts will look for baseline datasets in the +If the ‘-bd’ option is passed, the scripts will look for baseline datasets in the location passed to the -bd argument.
  • To generate a baseline dataset for a specific version (for regression testing),
    -
    use ‘-bg <version_name>’. The scripts will then place the baseline dataset +
    use ‘-bg <version_name>’. The scripts will then place the baseline dataset in $ICE_MACHINE_BASELINE/<version_name>/
  • -
    The ‘-testid’ flag allows users to specify a testing id that will be added to the
    -
    end of the case directory. For example, ”./create.case -m wolf -t smoke -testid t12 -p 4x1” +
    The ‘-testid’ flag allows users to specify a testing id that will be added to the
    +
    end of the case directory. For example, “./create.case -m wolf -t smoke -testid t12 -p 4x1” creates the directory wolf_smoke_gx3_4x1.t12. This flag is REQUIRED if using -t or -ts.
    • @@ -1931,118 +1928,242 @@

    3.6.4.6. Additional Details
    -

    3.6.5. Code compliance test

    -

    Additions and changes to CICE and Icepack are expected to be bit-for-bit -unless there is a strong justification for non-reproducibility, such as -a bug-fix or approved scientific alteration to existing code. However, -situations do arise when additions to CICE or Icepack are not -bit-for-bit, but are also not expected to change the science of CICE and -Icepack. In that instant, further evidence is required in the initial -testing phase to support the premise that code changes have not altered -the science of the model. To support this testing, a \(t\)-test is -being/has been implemented in the CICE testing infrastructure.

    -
    -

    3.6.5.1. Method

    -

    Welch’s two-sided \(t\)-test is used to help determine whether or -not two different simulations that should be identical are significantly -different for any grid cell of the CICE gx-1/3 domain for grid-cell -averaged sea ice thickness, \(h\), ice concentration, \(c\), and -pack velocity components \(\pmb{u}=\pmb{u}(u,v)\). In this -circumstance, we seek to determine whether or not the null hypothesis, -\(H_0\), is true. The null hypothesis is: Two simulations that are -not bit-for-bit identical are ostensibly the same at every model grid -point. The test begins from the standpoint that two CICE simulations -should be bit-for-bit but are suspected of only being different at the -level of computational innaccuracy. Therefore, we seek to limit a -\(t\)-test Type II error, where a test would erroneously confirm the -null hypothesis, \(H_0\). To that end, we choose to test the -hypothesis that grid-point means from CICE simulation ‘\(a\)’ are -different from CICE simulation ‘\(b\)’ at a relatively low -confidence interval. Formally, we test the hypothesis -\(H_0:\bar{x}_a=\bar{x}_b\), \(H_1:\bar{x}_a\neq\bar{x}_b\) for -each of the aforementioned variables at every model grid point using a -two-sided t-test with a 68, 80 and 95% confidence interval. Here, -\(\bar{x}{=}\tfrac{1}{n}\sum_{i=1}^n x_i\) is the time series mean -of \(n\) samples \(x_i\) representing \(h\), \(c\), -\(u\) or \(v\), and daily samples are used from 5-year -stand-alone CICE simulations. More frequent output is unnecessary, -because each of \(h\), \(c\), \(u\) and \(v\) typically -have a high degree of auto-correlation in sea ice models.

    -

    Due to the strong auto-correlation in geo-located sea ice time series, -we calculate a two-sided \(t\)-statistic to compare -\(\bar{x}_a\) and \(\bar{x}_b\), given their respective standard -deviations, \(\sigma_a\) and \(\sigma_b\), and effective sample -sizes, \(n'_a\) and \(n'_b\), following -[75] :

    +

    3.6.5. Code Compliance Test

    +

    A core tenet of CICE dycore and Icepack innovations is that they must not change +the physics and biogeochemistry of existing model configurations, notwithstanding +obsolete model components. Therefore, alterations to existing CICE Consortium code +must only fix demonstrable numerical or scientific inaccuracies or bugs, or be +necessary to introduce new science into the code. New physics and biogeochemistry +introduced into the model must not change model answers when switched off, and in +that case CICEcore and Icepack must reproduce answers bit-for-bit as compared to +previous simulations with the same namelist configurations. This bit-for-bit +requirement is common in Earth System Modeling projects, but often cannot be achieved +in practice because model additions may require changes to existing code. In this +circumstance, bit-for-bit reproducibility using one compiler may not be unachievable +on a different computing platform with a different compiler. Therefore, tools for +scientific testing of CICE code changes have been developed to accompany bit-for-bit +testing. These tools exploit the statistical properties of simulated sea ice thickness +to confirm or deny the null hypothesis, which is that new additions to the CICE dycore +and Icepack have not significantly altered simulated ice volume using previous model +configurations. Here we describe the CICE testing tools, which are applies to output +from five-year gx-1 simulations that use the standard CICE atmospheric forcing. +A scientific justification of the testing is provided in +[38].

    +
    +

    3.6.5.1. Two-Stage Paired Thickness Test

    +

    The first quality check aims to confirm the null hypotheses +\(H_0\!:\!\mu_d{=}0\) at every model grid point, given the mean +thickness difference \(\mu_d\) between paired CICE simulations +‘\(a\)’ and ‘\(b\)’ that should be identical. \(\mu_d\) is +approximated as +\(\bar{h}_{d}=\tfrac{1}{n}\sum_{i=1}^n (h_{ai}{-}h_{bi})\) for +\(n\) paired samples of ice thickness \(h_{ai}\) and +\(h_{bi}\) in each grid cell of the gx-1 mesh. Following +[84], the associated \(t\)-statistic +expects a zero mean, and is therefore

    -(1)\[t=\frac{\bar{x}_a - \bar{x}_b}{\sqrt{\frac{\sigma^2_a}{n'_a}+\frac{\sigma^2_b}{n'_b}}}.\]
    -

    The null hypothesis \(H_0:\bar{x}_a=\bar{x}_b\) is true when

    -
    -(2)\[-t_{crit}({1{-}\alpha/2},N)<t<t_{crit}({1{-}\alpha/2},N)\]
    -

    for critical \(t\)-distribution values, \(t_{crit}\), at the -\(\alpha\) significance level for effective degrees of freedom -\(N = n'_a + n'_b - 2\). At the 80% confidence interval, -\(\alpha=0.20\), with corresponding tabulated values of -\(t_{crit}(0.9,N)\) obtained from a \(t\)-distribution look-up -table. From [79] , we use an unbiased standard -deviation estimate,

    -
    -(3)\[\sigma=\sqrt{\frac{1}{n'-1}\sum_{i=1}^{n}(x_i-\bar{x})^2},\]
    -

    for the effective sample size,

    -
    -(4)\[n' \approx n \frac{1-r_1}{1+r_1},\]
    -

    where \(r_1\) is the lag-1 autocorrelation given by:

    -
    -(5)\[r_1=\frac{\sum\limits_{i=1}^{n-1}\big[(x_i-\bar{x}_{1:n-1})(x_{i+1}-\bar{x}_{2:n})\big]}{\sqrt{\sum\limits_{i=1}^{n-1} (x_i-\bar{x}_{1:n-1})^2 \sum\limits_{i=2}^{n} (x_i-\bar{x}_{2:n})^2 }}.\]
    -

    In equation (5), \(\bar{x}_{1:n-1}\) is -the mean of all samples except the last, and \(\bar{x}_{2:n}\) is -the mean of samples except the first, and both differ from the overall -mean \(\bar{x}\) in equations (1) -and (3), which we repeat here for clarity:

    +(1)\[t=\frac{\bar{h}_{d}}{\sigma_d/\sqrt{n_{eff}}}\]
    +

    given variance +\(\sigma_d^{\;2}=\frac{1}{n-1}\sum_{i=1}^{n}(h_{di}-\bar{h}_d)^2\) +of \(h_{di}{=}(h_{ai}{-}h_{bi})\) and effective sample size

    +
    +(2)\[n_{eff}{=}n\frac{({1-r_1})}{({1+r_1})}\]
    +

    for lag-1 autocorrelation:

    +
    +(3)\[r_1=\frac{\sum\limits_{i=1}^{n-1}\big[(h_{di}-\bar{h}_{d1:n-1})(h_{di+1}-\bar{h}_{d2:n})\big]}{\sqrt{\sum\limits_{i=1}^{n-1} (h_{di}-\bar{h}_{d1:n-1})^2 \sum\limits_{i=2}^{n} (h_{di}-\bar{h}_{d2:n})^2 }}.\]
    +

    Here, \(\bar{h}_{d1:n-1}\) is the mean of all samples except the +last, and \(\bar{h}_{d2:n}\) is the mean of samples except the +first, and both differ from the overall mean \(\bar{h}_d\) in +equations ((1)). That is:

    -(6)\[\bar{x}_{1:n-1}=\frac{1}{n{-}1} \sum \limits_{i=1}^{n-1} x_i,\quad -\bar{x}_{2:n}=\frac{1}{n{-}1} \sum \limits_{i=2}^{n} x_i,\quad -\bar{x}=\frac{1}{n} \sum \limits_{i=1}^{n} x_i\]
    -

    In applying equations (1) through (6), -we are accounting for the fact, however imperfectly, that a -\(t\)-test should be a comparison of the means from two series of -independent samples. The typical affect of applying these equations to -sea ice model output is that \(n' \ll n\). For that reason, we need -a lengthy time series to narrow the range of acceptable values -in (2). There is little point in using more frequent output -from CICE than daily instantaneous values, since this would have little -impact on decreasing \(r_1\) in (5).

    -

    Using these equations, a standard procedure in testing for -science-changing answers in CICE and Icepack is as follows: First, make -every attempt to obtain bit-for-bit reproducibility in the model code. -Once all available software-testing options have been exhausted, and the -source of the bit-for-bit test failure has been pinpointed, proceed with -the \(t\)-test documented above if the expectation is that code -alterations should not be science-changing. -Equations (1) through (6) are -implemented in the reverse order from which they are presented here, and -applied individually to daily samples of \(h\), \(c\), \(u\) -and \(v\) from 5-year time series at every model grid point: i) -Calculate \(\bar{x}_{1:n-1}\), \(\bar{x}_{2:n}\), and -\(\bar{x}\) in (6) for simulations \(a\) and -\(b\); ii) Compute (5), -(4) and (3), in that order, -for each simulation \(a\) and \(b\), and finally; iii) Determine -whether the null hypothesis is true at each model grid point in -(2) using equation (1) and a lookup -\(t\)-distribution table. Should \(H_0\) be confirmed at each -grid point, and for each variable \(h\), \(c\), \(u\) and -\(v\), this test contributes to evidence that changes to CICE and -Icepack code are unlikely to alter scientific results. To guard against -the possibility of a Type II error, the test should be performed for -several different confidence intervals, nominally set at 68, 80 and 95%, -the first and last of these values corresponding to \(\sigma\) and -\(2\sigma\) tests.

    +(4)\[\bar{h}_{d1:n-1}=\frac{1}{n{-}1} \sum \limits_{i=1}^{n-1} h_{di},\quad +\bar{h}_{d2:n}=\frac{1}{n{-}1} \sum \limits_{i=2}^{n} h_{di},\quad +\bar{h}_d=\frac{1}{n} \sum \limits_{i=1}^{n} {h}_{di}\]
    +

    Following [85], the effective sample size is +limited to \(n_{eff}\in[2,n]\). This definition of \(n_{eff}\) +assumes ice thickness evolves as an AR(1) process +[80], which can be justified by analyzing +the spectral density of daily samples of ice thickness from 5-year +records in CICE Consortium member models [38]. +The AR(1) approximation is inadmissible for paired velocity samples, +because ice drift possesses periodicity from inertia and tides +[29][43][59]. Conversely, +tests of paired ice concentration samples may be less sensitive to ice +drift than ice thickness. In short, ice thickness is the best variable +for CICE Consortium quality control (QC), and for the test of the mean +in particular.

    +

    Care is required in analyzing mean sea ice thickness changes using +((1)) with +\(N{=}n_{eff}{-}1\) degrees of freedom. +[85] demonstrate that the \(t\)-test in +((1)) becomes conservative when +\(n_{eff} < 30\), meaning that \(H_0\) may be erroneously +confirmed for highly auto-correlated series. Strong autocorrelation +frequently occurs in modeled sea ice thickness, and \(r_1>0.99\) is +possible in parts of the gx-1 domain for the five-year QC simulations. +In the event that \(H_0\) is confirmed but \(2\leq n_{eff}<30\), +the \(t\)-test progresses to the ‘Table Lookup Test’ of +[85], to check that the first-stage test +using ((1)) was not +conservative. The Table Lookup Test chooses critical \(t\) values +\(|t|<t_{crit}({1{-}\alpha/2},N)\) at the \(\alpha\) +significance level based on \(r_1\). It uses the conventional +\(t={\bar{h}_{d} \sqrt{n}}/{\sigma_d}\) statistic with degrees of +freedom \(N{=}n{-}1\), but with \(t_{crit}\) values generated +using the Monte Carlo technique described in +[85], and summarized in Table 1 for 5-year QC +simulations (\(N=1824\)) at the two-sided 80% confidence interval +(\(\alpha=0.2\)). We choose this interval to limit Type II errors, +whereby a QC test erroneously confirms \(H_0\).

    +

    Table 1 : Summary of two-sided \(t_{crit}\) values for the Table +Lookup Test of [85] at the 80% confidence +interval generated for \(N=1824\) degrees of freedom and lag-1 +autocorrelation \(r_1\).

    +

    Table 7
    + +++++++++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    Table 1
    \(r_1\)-0.050.00.20.40.50.60.70.80.90.950.970.99
    \(t_{crit}\)1.321.321.542.022.292.463.173.995.598.4410.8520.44
    +
    +

    +

    +
    +

    +
    +

    3.6.5.2. Quadratic Skill Compliance Test

    +

    In addition to the two-stage test of mean sea ice thickness, we also +check that paired simulations are highly correlated and have similar +variance using a skill metric adapted from +[72]. A general skill score applicable to +Taylor diagrams takes the form

    +
    +(5)\[S_m=\frac{4(1+R)^m}{({\hat{\sigma}_{f}+1/{\hat{\sigma}_{f}}})^2 (1+R_0)^m}\]
    +

    where \(m=1\) for variance-weighted skill, and \(m=4\) for +correlation-weighted performance, as given in equations (4) and (5) of +[72], respectively. We choose \(m=2\) to +balance the importance of variance and correlation reproduction in QC +tests, where \(\hat{\sigma}_{f}={\sigma_{b}}/{\sigma_{a}}\) is the ratio +of the standard deviations of simulations ‘\(b\)’ and ‘\(a\)’, +respectively, and simulation ‘\(a\)’ is the control. \(R_0\) is +the maximum possible correlation between two series for correlation +coefficient \(R\) calculated between respective thickness pairs +\(h_{a}\) and \(h_{b}\). Bit-for-bit reproduction of previous +CICE simulations means that perfect correlation is possible, and so +\(R_0=1\), giving the quadratic skill of run ‘\(b\)’ relative to +run ‘\(a\)’:

    +
    +(6)\[S=\bigg[ \frac{(1+R) (\sigma_a \sigma_b)}{({\sigma_a}^2 + {\sigma_b}^2)} \bigg]^2\]
    +

    This provides a skill score between 0 and 1. We apply this \(S\) +metric separately to the northern and southern hemispheres of the gx-1 +grid by area-weighting the daily thickness samples discussed in the +Two-Stage Paired Thickness QC Test. The hemispheric mean thickness over +a 5-year simulation for run ‘\(a\)’ is:

    +
    +(7)\[\bar{h}_{a}=\frac{1}{n} \sum_{i=1}^{n} \sum_{j=1}^{J} \ W_{j} \; h_{{a}_{i,j}}\]
    +

    at time sample \(i\) and grid point index \(j\), with an +equivalent equation for simulation ‘\(b\)’. \(n\) is the total +number of time samples (nominally \(n=1825\)) and \(J\) is the +total number of grid points on the gx-1 grid. \(W_j\) is the weight +attributed to each grid point according to its area \(A_{j}\), given +as

    +
    +(8)\[W_{j}=\frac{ A_{j} }{\sum_{j=1}^{J} A_{j}}\]
    +

    for all grid points within each hemisphere with one or more non-zero +thicknesses in one or both sets of samples \(h_{{a}_{i,j}}\) or +\(h_{{b}_{i,j}}\). The area-weighted variance for simulation +‘\(a\)’ is:

    +
    +(9)\[\sigma_a^{\;2}=\frac{\hat{J}}{(n\,\hat{J}-1)} \sum_{i=1}^{n} \sum_{j=1}^{J} W_{j} \, (h_{{a}_{i,j}}-\bar{h}_{a})^2\]
    +

    where \(\hat{J}\) is the number of non-zero \(W_j\) weights, +and \(\sigma_b\) is calculated equivalently for run ‘\(b\)’. In +this context, \(R\) becomes a weighted correlation coefficient, +calculated as

    +
    +(10)\[R=\frac{\textrm{cov}(h_{a},h_{b})}{\sigma_a \; \sigma_b}\]
    +

    given the weighted covariance

    +
    +(11)\[\textrm{cov}(h_{a},h_{b})=\frac{\hat{J}}{(n\,\hat{J}-1)} \sum_{i=1}^{n} \sum_{j=1}^{J} W_{j} \, (h_{{a}_{i,j}}-\bar{h}_{a}) (h_{{b}_{i,j}}-\bar{h}_{b}).\]
    +

    Using equations ((6)) +to ((11)), the skill +score \(S\) is calculated separately for the northern and southern +hemispheres, and must exceed a critical value nominally set to +\(S_{crit}=0.99\) to pass the test. Practical illustrations of this +test and the Two-Stage test described in the previous section are +provided in [38].

    -

    3.6.5.2. Practical Testing Procedure

    -

    To be placed here: Write up of how to actually do this test within the -testing software to be added by Elizabeth, Rick, Matt, Tony et al....

    +

    3.6.5.3. Practical Testing Procedure

    +

    The CICE code compliance test is performed by running a python script (cice.t-test.py). +In order to run the script, the following requirements must be met:

    +
      +
    • Python v2.7 or later
      • +
    • netCDF Python package
      • +
    • numpy Python package
      • +
    +

    In order to generate the files necessary for the compliance test, test cases should be +created with the ttest option (i.e., -s ttest) when running create.case. This +option results in daily, non-averaged history files being written for a 5 year simulation.

    +

    To run the compliance test:

    +
    cp configuration/scripts/tests/QC/cice.t-test.py .
+./cice.t-test.py /path/to/baseline/history /path/to/test/history
+
    +
    +

    The script will produce output similar to:

    +
    +
    +
    INFO:__main__:Number of files: 1825
    +
    INFO:__main__:Two-Stage Test Passed
    +
    INFO:__main__:Quadratic Skill Test Passed for Northern Hemisphere
    +
    INFO:__main__:Quadratic Skill Test Passed for Southern Hemisphere
    +
    INFO:__main__:
    +
    INFO:__main__:Quality Control Test PASSED
    +
    +
    +

    Additionally, the exit code from the test (echo $?) will be 0 if the test passed, +and 1 if the test failed.

    Implementation notes: 1) Provide a pass/fail on each of the confidence intervals, 2) Facilitate output of a bitmap for each test so that locations of failures can be identified.

    @@ -2051,8 +2172,8 @@

    3.6.5.2. Practical Testing Procedure

    3.7. Table of namelist options

    - - +
    Table 8
    +@@ -2330,27 +2451,27 @@

    3.6.5.2. Practical Testing Procedure

    + - + - + - + - + @@ -2687,18 +2808,18 @@

    3.6.5.2. Practical Testing Procedure

    - + - + - + @@ -2713,7 +2834,7 @@

    3.6.5.2. Practical Testing Procedure

    - + @@ -2777,12 +2898,12 @@

    3.6.5.2. Practical Testing Procedure

    - + - + @@ -2885,12 +3006,12 @@

    3.6.5.2. Practical Testing Procedure

    - + - + @@ -2988,34 +3109,24 @@

    3.6.5.2. Practical Testing Procedure

    + - + - + - + - - - - - - - - - - - + - + - + - + @@ -3023,31 +3134,61 @@

    3.6.5.2. Practical Testing Procedure

    + + + + + + - + - + - + - + - + - + + + + + + + + + + + + + + + + + + + + + + + + + + @@ -3210,7 +3351,7 @@

    3.6.5.2. Practical Testing Procedure

    - + @@ -3234,7 +3375,7 @@

    3.6.5.2. Practical Testing Procedure

    - + @@ -3404,24 +3545,11 @@

    Table Of Contents

  • 3. User Guide
    • - + @@ -3473,7 +3470,7 @@

    Navigation

     \ No newline at end of file diff --git a/index.html b/index.html index f7aec5944..7dedab2db 100644 --- a/index.html +++ b/index.html @@ -1,16 +1,13 @@ + - - CICE Documentation — CICE-Consortium 0.0.1 documentation - - - + - + \ No newline at end of file diff --git a/objects.inv b/objects.inv index 333ac9fd7..4cbc1f5b0 100644 Binary files a/objects.inv and b/objects.inv differ diff --git a/search.html b/search.html index e953ca477..45ccbaf94 100644 --- a/search.html +++ b/search.html @@ -1,16 +1,13 @@ + - - Search — CICE-Consortium 0.0.1 documentation - - - + - + - +
    Table 8
    history\_dir
    history_dir path/ path to history output directory  
    history\_file
    history_file filename prefix output file for history ‘iceh’
    write\_ic
    write_ic true/false write initial condition  
    incond\_dir
    incond_dir path/ path to initial condition directory  
    incond\_file
    incond_file filename prefix output file for initial condition ‘iceh’conduct MU71conductivity [50]conductivity [53]  
      bubblyconductivity [55]conductivity [58]  
    a_rapid_mode real brine channel diameter0.5x10:math:^{-3} m0.5x10 \(^{-3}\) m
    Rac_rapid_mode realdSdt_slow_mode real drainage strength parameter-1.5x10:math:^{-7} m/s/K-1.5x10 \(^{-7}\) m/s/K
    phi_c_slow_mode \(0<\phi_c < 1\)kstrength 0ice strength formulation [26]ice strength formulation [26] 1
      1ice strength formulation [57]ice strength formulation [61]  
    krdg_particR_pnd real... for ponded sea ice albedo …… for ponded sea ice albedo …  
    R_snw real... for snow (broadband albedo) …… for snow (broadband albedo) …  
    dT_mltrestart_hbrine
    tr_zaero true/falserestart tracer values from filevertical aerosol tracers  
    skl_bgc
    modal_aero true/falsebiogeochemistrymodal aersols  
    bgc_flux_typeJin2006ice–ocean flux velocity of [37] 
     constantconstant ice–ocean flux velocity 
    restart_bgc
    restore_bgc true/falserestart tracer values from filerestore bgc to data  
    restore_bgc
    ``solve_zsal` true/falserestore nitrate/silicate to dataupdate salinity tracer profile  
    bgc_data_dirsil_data_type
    skl_bgctrue/falsebiogeochemistry 
    sil_data_type default default forcing value for silicate  
     
      climsilicate forcing from ocean climatology [23]silicate forcing from ocean climatology [23]  
    nit_data_type
    nit_data_type default default forcing value for nitrate  
     
      climnitrate forcing from ocean climatology [23]nitrate forcing from ocean climatology [23]  
     
      sss nitrate forcing equals salinity  
    fe_data_typedefaultdefault forcing value for iron 
     climiron forcing from ocean climatology 
    bgc_flux_typeJin2006ice–ocean flux velocity of [39] 
     constantconstant ice–ocean flux velocity 
    restart_bgctrue/falserestart tracer values from file 
    tr_bgc_C_sk true/false algal carbon tracertfrz_option minus1p8constant ocean freezing temperature (\(-1.8\degC\))constant ocean freezing temperature (\(-1.8^{\circ} C\))  
      Cdn\_ocnCdn_ocn variable ocean heat transfer coefficient  
    kstrength\(\bullet\) ice stength formulation (1= [57], 0 = [26])\(\bullet\) ice stength formulation (1= [61], 0 = [26]) 1  
    W.D. Hibler and K. Bryan. A diagnostic ice-ocean model. J. Phys. Oceanogr., 17:987–1015, 1987. URL: http://dx.doi.org/10.1175/1520-0485(1987)017<0987:ADIM>2.0.CO;2.
    + + + + + +
    [29]W.D. Hibler, A. Roberts, P. Heil, A.Y. Proshutinsky, H.L. Simmons, and J. Lovick. Modeling M2 tidal variability in Arctic sea-ice drift and deformation. Ann. Glaciol., 2006. doi:10.3189/172756406781811178.
    - +
    [29]M.M. Holland, D.A. Bailey, B.P. Briegleb, B. Light, and E. Hunke. Improved sea ice shortwave radiation physics in CCSM4: The impact of melt ponds and aerosols on Arctic sea ice. J. Climate, 25:1413–1430, 2012. URL: http://dx.doi.org/10.1175/JCLI-D-11-00078.1.
    [30]M.M. Holland, D.A. Bailey, B.P. Briegleb, B. Light, and E. Hunke. Improved sea ice shortwave radiation physics in CCSM4: The impact of melt ponds and aerosols on Arctic sea ice. J. Climate, 25:1413–1430, 2012. URL: http://dx.doi.org/10.1175/JCLI-D-11-00078.1.
    - +
    [30]E.C. Hunke. Viscous-plastic sea ice dynamics with the EVP model: Linearization issues. J. Comp. Phys., 170:18–38, 2001. URL: http://dx.doi.org/10.1006/jcph.2001.6710.
    [31]E.C. Hunke. Viscous-plastic sea ice dynamics with the EVP model: Linearization issues. J. Comp. Phys., 170:18–38, 2001. URL: http://dx.doi.org/10.1006/jcph.2001.6710.
    - +
    [31]E.C. Hunke and C.M. Bitz. Age characteristics in a multidecadal Arctic sea ice simulation. J. Geophys. Res. Oceans, 2009. URL: http://dx.doi.org/10.1029/2008JC005186.
    [32]E.C. Hunke and C.M. Bitz. Age characteristics in a multidecadal Arctic sea ice simulation. J. Geophys. Res. Oceans, 2009. URL: http://dx.doi.org/10.1029/2008JC005186.
    - +
    [32]E.C. Hunke and J.K. Dukowicz. An elastic-viscous-plastic model for sea ice dynamics. J. Phys. Oceanogr., 27:1849–1867, 1997. URL: http://dx.doi.org/10.1175/1520-0485(1997)027<1849:AEVPMF>2.0.CO;2.
    [33]E.C. Hunke and J.K. Dukowicz. An elastic-viscous-plastic model for sea ice dynamics. J. Phys. Oceanogr., 27:1849–1867, 1997. URL: http://dx.doi.org/10.1175/1520-0485(1997)027<1849:AEVPMF>2.0.CO;2.
    - +
    [33]E.C. Hunke and J.K. Dukowicz. The Elastic-Viscous-Plastic sea ice dynamics model in general orthogonal curvilinear coordinates on a sphere—Effect of metric terms. Mon. Wea. Rev., 130:1848–1865, 2002. URL: http://dx.doi.org/10.1175/1520-0493(2002)130<1848:TEVPSI>2.0.CO;2.
    [34]E.C. Hunke and J.K. Dukowicz. The Elastic-Viscous-Plastic sea ice dynamics model in general orthogonal curvilinear coordinates on a sphere—Effect of metric terms. Mon. Wea. Rev., 130:1848–1865, 2002. URL: http://dx.doi.org/10.1175/1520-0493(2002)130<1848:TEVPSI>2.0.CO;2.
    - +
    [34]E.C. Hunke and J.K. Dukowicz. The sea ice momentum equation in the free drift regime. Technical Report LA-UR-03-2219, Los Alamos National Laboratory, 2003. URL: https://github.com/CICE-Consortium/CICE/blob/master/doc/PDF/LAUR-03-2219.pdf.
    [35]E.C. Hunke and J.K. Dukowicz. The sea ice momentum equation in the free drift regime. Technical Report LA-UR-03-2219, Los Alamos National Laboratory, 2003. URL: https://github.com/CICE-Consortium/CICE/blob/master/doc/PDF/LAUR-03-2219.pdf.
    - +
    [35]E.C. Hunke, D.A. Hebert, and O. Lecomte. Level-ice melt ponds in the Los Alamos Sea Ice Model, CICE. Ocean Modelling, 71:26–42, 2013. URL: http://dx.doi.org/10.1016/j.ocemod.2012.11.008.
    [36]E.C. Hunke, D.A. Hebert, and O. Lecomte. Level-ice melt ponds in the Los Alamos Sea Ice Model, CICE. Ocean Modelling, 71:26–42, 2013. URL: http://dx.doi.org/10.1016/j.ocemod.2012.11.008.
    - + + +
    [36]E.C. Hunke and Y. Zhang. A comparison of sea ice dynamics models at high resolution. Mon. Wea. Rev., 127:396–408, 1999. URL: http://dx.doi.org/10.1175/1520-0493(1999)127<0396:ACOSID>2.0.CO;2.
    [37]E.C. Hunke and Y. Zhang. A comparison of sea ice dynamics models at high resolution. Mon. Wea. Rev., 127:396–408, 1999. URL: http://dx.doi.org/10.1175/1520-0493(1999)127<0396:ACOSID>2.0.CO;2.
    + + + +
    [38]Elizabeth Hunke, Andrew Roberts, Richard Allard, Jean-François Lemieux, Matthew Turner, Tony Craig, Alice DuVivier, David Bailey, Marika Holland, Michael Winton, Frederic Dupont, and Robert Grumbine. The CICE Consortium Sea Ice Modeling Suite. In Prep.
    - +
    [37]M. Jin, C. Deal, J. Wang, K.H. Shin, N. Tanaka, T.E. Whiteledge, S.H. Lee, and R.R. Gradinger. Controls of the landfast ice-ocean ecosystem offshore Barrow, Alaska. Ann. Glaciol., 44:63–72, 2006. URL: https://github.com/CICE-Consortium/CICE/blob/master/doc/PDF/JDWSTWLG06.pdf.
    [39]M. Jin, C. Deal, J. Wang, K.H. Shin, N. Tanaka, T.E. Whiteledge, S.H. Lee, and R.R. Gradinger. Controls of the landfast ice-ocean ecosystem offshore Barrow, Alaska. Ann. Glaciol., 44:63–72, 2006. URL: https://github.com/CICE-Consortium/CICE/blob/master/doc/PDF/JDWSTWLG06.pdf.
    - +
    [38]R.E. Jordan, E.L. Andreas, and A.P. Makshtas. Heat budget of snow-covered sea ice at North Pole 4. J. Geophys. Res. Oceans, 104(C4):7785–7806, 1999. URL: http://dx.doi.org/10.1029/1999JC900011.
    [40]R.E. Jordan, E.L. Andreas, and A.P. Makshtas. Heat budget of snow-covered sea ice at North Pole 4. J. Geophys. Res. Oceans, 104(C4):7785–7806, 1999. URL: http://dx.doi.org/10.1029/1999JC900011.
    - +
    [39]B.G. Kauffman and W.G. Large. The CCSM coupler, version 5.0.1. NCAR Tech. Note, 2002. URL: https://github.com/CICE-Consortium/CICE/blob/master/doc/PDF/KL_NCAR2002.pdf.
    [41]B.G. Kauffman and W.G. Large. The CCSM coupler, version 5.0.1. NCAR Tech. Note, 2002. URL: https://github.com/CICE-Consortium/CICE/blob/master/doc/PDF/KL_NCAR2002.pdf.
    - + + +
    [40]D. Lavoie, K. Denman, and C. Michel. Modeling ice algal growth and decline in a seasonally ice- covered region of the Arctic (Resolute Passage, Canadian Archipelago). J. Geophys. Res. Oceans, 2005. URL: http://dx.doi.org/10.1029/2005JC002922.
    [42]D. Lavoie, K. Denman, and C. Michel. Modeling ice algal growth and decline in a seasonally ice- covered region of the Arctic (Resolute Passage, Canadian Archipelago). J. Geophys. Res. Oceans, 2005. URL: http://dx.doi.org/10.1029/2005JC002922.
    + + + +
    [43]Matti Leppäranta, Annu Oikkonen, Kunio Shirasawa, and Yasushi Fukamachi. A treatise on frequency spectrum of drift ice velocity. Cold Reg. Sci. Technol., 76-77:83–91, jun 2012. doi:10.1016/j.coldregions.2011.12.005.
    - +
    [41]W.H. Lipscomb. Modeling the Thickness Distribution of Arctic Sea Ice. Dept. of Atmospheric Sciences University of Washington, Seattle, 1998. PhD thesis. URL: http://hdl.handle.net/1773/10081.
    [44]W.H. Lipscomb. Modeling the Thickness Distribution of Arctic Sea Ice. Dept. of Atmospheric Sciences University of Washington, Seattle, 1998. PhD thesis. URL: http://hdl.handle.net/1773/10081.
    - +
    [42]W.H. Lipscomb. Remapping the thickness distribution in sea ice models. J. Geophys. Res. Oceans, 106:13989–14000, 2001. URL: http://dx.doi.org/10.1029/2000JC000518.
    [45]W.H. Lipscomb. Remapping the thickness distribution in sea ice models. J. Geophys. Res. Oceans, 106:13989–14000, 2001. URL: http://dx.doi.org/10.1029/2000JC000518.
    - +
    [43]W.H. Lipscomb and E.C. Hunke. Modeling sea ice transport using incremental remapping. Mon. Wea. Rev., 132:1341–1354, 2004. URL: http://dx.doi.org/10.1175/1520-0493(2004)132<1341:MSITUI>2.0.CO;2.
    [46]W.H. Lipscomb and E.C. Hunke. Modeling sea ice transport using incremental remapping. Mon. Wea. Rev., 132:1341–1354, 2004. URL: http://dx.doi.org/10.1175/1520-0493(2004)132<1341:MSITUI>2.0.CO;2.
    - +
    [44]W.H. Lipscomb, E.C. Hunke, W. Maslowski, and J. Jakacki. Ridging, strength, and stability in high-resolution sea ice models. J. Geophys. Res. Oceans, 2007. URL: http://dx.doi.org/10.1029/2005JC003355.
    [47]W.H. Lipscomb, E.C. Hunke, W. Maslowski, and J. Jakacki. Ridging, strength, and stability in high-resolution sea ice models. J. Geophys. Res. Oceans, 2007. URL: http://dx.doi.org/10.1029/2005JC003355.
    - +
    [45]P. Lu, Z. Li, B. Cheng, and M. Lepparanta. A parametrization fo the ice-ocean drag coefficient. J. Geophys. Res. Oceans, 2011. URL: http://dx.doi.org/10.1029/2010JC006878.
    [48]P. Lu, Z. Li, B. Cheng, and M. Lepparanta. A parametrization fo the ice-ocean drag coefficient. J. Geophys. Res. Oceans, 2011. URL: http://dx.doi.org/10.1029/2010JC006878.
    - +
    [46]C. Lüpkes, V.M. Gryanik, J. Hartmann, and E.L. Andreas. A parametrization, based on sea ice morphology, of the neutral atmospheric drag coefficients for weather prediction and climate models. J. Geophys. Res. Atmos., 2012. URL: http://dx.doi.org/10.1029/2012JD017630.
    [49]C. Lüpkes, V.M. Gryanik, J. Hartmann, and E.L. Andreas. A parametrization, based on sea ice morphology, of the neutral atmospheric drag coefficients for weather prediction and climate models. J. Geophys. Res. Atmos., 2012. URL: http://dx.doi.org/10.1029/2012JD017630.
    - +
    [47]G.A. Maykut. Large-scale heat exchange and ice production in the central Arctic. J. Geophys. Res. Oceans, 87:7971–7984, 1982. URL: http://dx.doi.org/10.1029/JC087iC10p07971.
    [50]G.A. Maykut. Large-scale heat exchange and ice production in the central Arctic. J. Geophys. Res. Oceans, 87:7971–7984, 1982. URL: http://dx.doi.org/10.1029/JC087iC10p07971.
    - +
    [48]G.A. Maykut and M.G. McPhee. Solar heating of the Arctic mixed layer. J. Geophys. Res. Oceans, 100:24691–24703, 1995. URL: http://dx.doi.org/10.1029/95JC02554.
    [51]G.A. Maykut and M.G. McPhee. Solar heating of the Arctic mixed layer. J. Geophys. Res. Oceans, 100:24691–24703, 1995. URL: http://dx.doi.org/10.1029/95JC02554.
    - +
    [49]G.A. Maykut and D.K. Perovich. The role of shortwave radiation in the summer decay of a sea ice cover. J. Geophys. Res. Oceans, 92:7032–7044, 1987. URL: http://dx.doi.org/10.1029/JC092iC07p07032.
    [52]G.A. Maykut and D.K. Perovich. The role of shortwave radiation in the summer decay of a sea ice cover. J. Geophys. Res. Oceans, 92:7032–7044, 1987. URL: http://dx.doi.org/10.1029/JC092iC07p07032.
    - +
    [50]G.A. Maykut and N. Untersteiner. Some results from a time dependent thermodynamic model of sea ice. J. Geophys. Res., 76:1550–1575, 1971. URL: http://dx.doi.org/10.1029/JC076i006p01550.
    [53]G.A. Maykut and N. Untersteiner. Some results from a time dependent thermodynamic model of sea ice. J. Geophys. Res., 76:1550–1575, 1971. URL: http://dx.doi.org/10.1029/JC076i006p01550.
    - +
    [51]R.J. Murray. Explicit generation of orthogonal grids for ocean models. J. Comput. Phys., 126:251–273, 1996. URL: http://dx.doi.org/10.1006/jcph.1996.0136.
    [54]R.J. Murray. Explicit generation of orthogonal grids for ocean models. J. Comput. Phys., 126:251–273, 1996. URL: http://dx.doi.org/10.1006/jcph.1996.0136.
    - +
    [52]D. Notz. Thermodynamic and Fluid-Dynamical Processes in Sea Ice. University of Cambridge, UK, 2005. PhD thesis. URL: http://ulmss-newton.lib.cam.ac.uk/vwebv/holdingsInfo?bibId=27224.
    [55]D. Notz. Thermodynamic and Fluid-Dynamical Processes in Sea Ice. University of Cambridge, UK, 2005. PhD thesis. URL: http://ulmss-newton.lib.cam.ac.uk/vwebv/holdingsInfo?bibId=27224.
    - +
    [53]N. Ono. Specific heat and heat of fusion of sea ice. In H. Oura, editor, Physics of Snow and Ice, volume I, pages 599–610. Institute of Low Temperature Science, Hokkaido, Japan, 1967.
    [56]N. Ono. Specific heat and heat of fusion of sea ice. In H. Oura, editor, Physics of Snow and Ice, volume I, pages 599–610. Institute of Low Temperature Science, Hokkaido, Japan, 1967.
    - +
    [54]C.L. Parkinson and W.M. Washington. A large-scale numerical model of sea ice. J. Geophys. Res. Oceans, 84(C1):331–337, 1979. URL: http://dx.doi.org/10.1029/JC084iC01p00311.
    [57]C.L. Parkinson and W.M. Washington. A large-scale numerical model of sea ice. J. Geophys. Res. Oceans, 84(C1):331–337, 1979. URL: http://dx.doi.org/10.1029/JC084iC01p00311.
    - + + +
    [55]D.J. Pringle, H. Eicken, H.J. Trodahl, and L.G.E. Backstrom. Thermal conductivity of landfast Antarctic and Arctic sea ice. J. Geophys. Res. Oceans, 2007. URL: http://dx.doi.org/10.1029/2006JC003641.
    [58]D.J. Pringle, H. Eicken, H.J. Trodahl, and L.G.E. Backstrom. Thermal conductivity of landfast Antarctic and Arctic sea ice. J. Geophys. Res. Oceans, 2007. URL: http://dx.doi.org/10.1029/2006JC003641.
    + + + +
    [59]Andrew F. Roberts, Anthony Craig, Wieslaw Maslowski, Robert Osinski, Alice Duvivier, Mimi Hughes, Bart Nijssen, John J. Cassano, and Michael Brunke. Simulating transient ice – ocean Ekman transport in the Regional Arctic System Model and Community Earth System Model. Ann. Glaciol., 56(69):211–228, 2015. doi:10.3189/2015AoG69A760.
    - +
    [56]A. Rosati and K. Miyakoda. A general circulation model for upper ocean simulation. J. Phys. Oceanogr., 18:1601–1626, 1988. URL: https://doi.org/10.1175/1520-0485(1988)018<1601:AGCMFU>2.0.CO;2.
    [60]A. Rosati and K. Miyakoda. A general circulation model for upper ocean simulation. J. Phys. Oceanogr., 18:1601–1626, 1988. URL: https://doi.org/10.1175/1520-0485(1988)018<1601:AGCMFU>2.0.CO;2.
    - +
    [57]D.A. Rothrock. The energetics of plastic deformation of pack ice by ridging. J. Geophys. Res., 80:4514–4519, 1975. URL: http://dx.doi.org/10.1029/JC080i033p04514.
    [61]D.A. Rothrock. The energetics of plastic deformation of pack ice by ridging. J. Geophys. Res., 80:4514–4519, 1975. URL: http://dx.doi.org/10.1029/JC080i033p04514.
    - +
    [58]E.M. Schulson. Brittle failure of ice. Eng. Fract. Mech., 68:1839–1887, 2001. URL: http://dx.doi.org/10.1016/S0013-7944(01)00037-6.
    [62]E.M. Schulson. Brittle failure of ice. Eng. Fract. Mech., 68:1839–1887, 2001. URL: http://dx.doi.org/10.1016/S0013-7944(01)00037-6.
    - +
    [59]W. Schwarzacher. Pack ice studies in the Arctic Ocean. J. Geophys. Res., 64:2357–2367, 1959. URL: http://dx.doi.org/10.1029/JZ064i012p02357.
    [63]W. Schwarzacher. Pack ice studies in the Arctic Ocean. J. Geophys. Res., 64:2357–2367, 1959. URL: http://dx.doi.org/10.1029/JZ064i012p02357.
    - +
    [60]A.J. Semtner. A Model for the Thermodynamic Growth of Sea Ice in Numerical Investigations of Climate. J. Phys. Oceanogr., 6:379–389, 1976. URL: http://dx.doi.org/10.1175/1520-0485(1976)006<0379:AMFTTG>2.0.CO;2.
    [64]A.J. Semtner. A Model for the Thermodynamic Growth of Sea Ice in Numerical Investigations of Climate. J. Phys. Oceanogr., 6:379–389, 1976. URL: http://dx.doi.org/10.1175/1520-0485(1976)006<0379:AMFTTG>2.0.CO;2.
    - +
    [61]G. Siedler and H. Peters. Physical properties (general) of sea water. In Landolt-Börnstein: Numerical data and functional relationships in science and technology, New Series V/3a, pages 233–264. Springer, 1986.
    [65]G. Siedler and H. Peters. Physical properties (general) of sea water. In Landolt-Börnstein: Numerical data and functional relationships in science and technology, New Series V/3a, pages 233–264. Springer, 1986.
    - +
    [62]R.D. Smith, J.K. Dukowicz, and R.C. Malone. Parallel ocean general circulation modeling. Physica D, 60(1):38–61, 1992. URL: https://doi.org/10.1016/0167-2789(92)90225-C.
    [66]R.D. Smith, J.K. Dukowicz, and R.C. Malone. Parallel ocean general circulation modeling. Physica D, 60(1):38–61, 1992. URL: https://doi.org/10.1016/0167-2789(92)90225-C.
    - +
    [63]R.D. Smith, S. Kortas, and B. Meltz. Curvilinear coordinates for global ocean models. Technical Report LA-UR-95-1146, Los Alamos National Laboratory, 1995. URL: https://github.com/CICE-Consortium/CICE/blob/master/doc/PDF/LAUR-95-1146.pdf.
    [67]R.D. Smith, S. Kortas, and B. Meltz. Curvilinear coordinates for global ocean models. Technical Report LA-UR-95-1146, Los Alamos National Laboratory, 1995. URL: https://github.com/CICE-Consortium/CICE/blob/master/doc/PDF/LAUR-95-1146.pdf.
    - +
    [64]M. Steele. Sea ice melting and floe geometry in a simple ice-ocean model. J. Geophys. Res. Oceans, 97:17729–17738, 1992. URL: http://dx.doi.org/10.1029/92JC01755.
    [68]M. Steele. Sea ice melting and floe geometry in a simple ice-ocean model. J. Geophys. Res. Oceans, 97:17729–17738, 1992. URL: http://dx.doi.org/10.1029/92JC01755.
    - +
    [65]M. Steele, J. Zhang, D. Rothrock, and H. Stern. The force balance of sea ice in a numerical model of the Arctic Ocean. J. Geophys. Res. Oceans, 102(C9):21061–21079, 1997. URL: http://dx.doi.org/10.1029/97JC01454.
    [69]M. Steele, J. Zhang, D. Rothrock, and H. Stern. The force balance of sea ice in a numerical model of the Arctic Ocean. J. Geophys. Res. Oceans, 102(C9):21061–21079, 1997. URL: http://dx.doi.org/10.1029/97JC01454.
    - +
    [66]J. Stefels, M. Steinke, S. Turner, G. Malin, and S. Belviso. Environmental constraints on the production and removal of the climatically active gas dimethylsulphide (DMS) and implications for ecosystem modelling. Biogeochemistry, 83:245–275, 2007. URL: http://dx.doi.org/10.1007/978-1-4020-6214-8_18.
    [70]J. Stefels, M. Steinke, S. Turner, G. Malin, and S. Belviso. Environmental constraints on the production and removal of the climatically active gas dimethylsulphide (DMS) and implications for ecosystem modelling. Biogeochemistry, 83:245–275, 2007. URL: http://dx.doi.org/10.1007/978-1-4020-6214-8_18.
    - + + +
    [67]A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice-Hall, 1971. Englewood Cliffs, New Jersey.
    [71]A.H. Stroud. Approximate Calculation of Multiple Integrals. Prentice-Hall, 1971. Englewood Cliffs, New Jersey.
    + + + +
    [72]Karl E Taylor. Summarizing multiple aspects of model performance. J. Geophys. Res., 106(D7):7183–7192, 2001.
    - +
    [68]P.D. Taylor and D.L. Feltham. A model of melt pond evolution on sea ice. J. Geophys. Res. Oceans, 2004. URL: http://dx.doi.org/10.1029/2004JC002361.
    [73]P.D. Taylor and D.L. Feltham. A model of melt pond evolution on sea ice. J. Geophys. Res. Oceans, 2004. URL: http://dx.doi.org/10.1029/2004JC002361.
    - +
    [69]A.S. Thorndike, D.A. Rothrock, G.A. Maykut, and R. Colony. The thickness distribution of sea ice. J. Geophys. Res., 80:4501–4513, 1975. URL: http://dx.doi.org/10.1029/JC080i033p04501.
    [74]A.S. Thorndike, D.A. Rothrock, G.A. Maykut, and R. Colony. The thickness distribution of sea ice. J. Geophys. Res., 80:4501–4513, 1975. URL: http://dx.doi.org/10.1029/JC080i033p04501.
    - +
    [70]H.J. Trodahl, S.O.F. Wilkinson, M.J. McGuinness, and T.G. Haskeel. Thermal conductivity of sea ice: dependence on temperature and depth. Geophys. Res. Lett., 28:1279–1282, 2001. URL: http://dx.doi.org/10.1029/2000GL012088.
    [75]H.J. Trodahl, S.O.F. Wilkinson, M.J. McGuinness, and T.G. Haskeel. Thermal conductivity of sea ice: dependence on temperature and depth. Geophys. Res. Lett., 28:1279–1282, 2001. URL: http://dx.doi.org/10.1029/2000GL012088.
    - +
    [71]M. Tsamados, D.L. Feltham, D. Schroeder, D. Flocco, S.L. Farrell, N.T. Kurtz, S.W. Laxon, and S. Bacon. Impact of variable atmospheric and oceanic form drag on simulations of Arctic sea ice. J. Phys. Oceanogr., 44:1329–1353, 1999. URL: https://doi.org/10.1175/JPO-D-13-0215.1.
    [76]M. Tsamados, D.L. Feltham, D. Schroeder, D. Flocco, S.L. Farrell, N.T. Kurtz, S.W. Laxon, and S. Bacon. Impact of variable atmospheric and oceanic form drag on simulations of Arctic sea ice. J. Phys. Oceanogr., 44:1329–1353, 1999. URL: https://doi.org/10.1175/JPO-D-13-0215.1.
    - +
    [72]M. Tsamados, D.L. Feltham, and A.V. Wilchinsky. Impact of a new anisotropic rheology on simulations of Arctic sea ice. J. Geophys. Res. Oceans, 118:91–107, 2013. URL: http://dx.doi.org/10.1029/2012JC007990.
    [77]M. Tsamados, D.L. Feltham, and A.V. Wilchinsky. Impact of a new anisotropic rheology on simulations of Arctic sea ice. J. Geophys. Res. Oceans, 118:91–107, 2013. URL: http://dx.doi.org/10.1029/2012JC007990.
    - +
    [73]A.K. Turner, E.C. Hunke, and C.M. Bitz. Two modes of sea-ice gravity drainage: a parameterization for large-scale modeling. J. Geophys. Res. Oceans, 118:2279–2294, 2013. URL: http://dx.doi.org/10.1002/jgrc.20171.
    [78]A.K. Turner, E.C. Hunke, and C.M. Bitz. Two modes of sea-ice gravity drainage: a parameterization for large-scale modeling. J. Geophys. Res. Oceans, 118:2279–2294, 2013. URL: http://dx.doi.org/10.1002/jgrc.20171.
    - +
    [74]N. Untersteiner. Calculations of temperature regime and heat budget of sea ice in the Central Arctic. J. Geophys. Res., 69:4755–4766, 1964. URL: http://dx.doi.org/10.1029/JZ069i022p04755.
    [79]N. Untersteiner. Calculations of temperature regime and heat budget of sea ice in the Central Arctic. J. Geophys. Res., 69:4755–4766, 1964. URL: http://dx.doi.org/10.1029/JZ069i022p04755.
    - +
    - +
    [75]H. von Storch and F.W. Zwiers. Statistical Analysis in Climate Research. Cambridge University Press, 1999. Cambridge, UK.
    [80]Hans von Storch and Francis W Zwiers. Statistical Analysis in Climate Research. Cambridge University Press, 1999.
    - +
    [76]J. Weiss and E.M. Schulson. Coulombic faulting from the grain scale to the geophysical scale: lessons from ice. J. of Phys. D: Appl. Phys., 42:214017, 2009. URL: http://stacks.iop.org/0022-3727/42/i=21/a=214017.
    [81]J. Weiss and E.M. Schulson. Coulombic faulting from the grain scale to the geophysical scale: lessons from ice. J. of Phys. D: Appl. Phys., 42:214017, 2009. URL: http://stacks.iop.org/0022-3727/42/i=21/a=214017.
    - +
    [77]A.V. Wilchinsky and D.L. Feltham. Dependence of sea ice yield-curve shape on ice thickness. J. Phys. Oceanogr., 34:2852–2856, 2004. URL: http://dx.doi.org/10.1175/JPO2667.1.
    [82]A.V. Wilchinsky and D.L. Feltham. Dependence of sea ice yield-curve shape on ice thickness. J. Phys. Oceanogr., 34:2852–2856, 2004. URL: http://dx.doi.org/10.1175/JPO2667.1.
    - + + +
    [78]A.V. Wilchinsky and D.L. Feltham. Modelling the rheology of sea ice as a collection of diamond-shaped floes. J. Non-Newtonian Fluid Mech., 138:22–32, 2006. URL: http://dx.doi.org/10.1016/j.jnnfm.2006.05.001.
    [83]A.V. Wilchinsky and D.L. Feltham. Modelling the rheology of sea ice as a collection of diamond-shaped floes. J. Non-Newtonian Fluid Mech., 138:22–32, 2006. URL: http://dx.doi.org/10.1016/j.jnnfm.2006.05.001.
    + + + +
    [84]Daniel S Wilks. Statistical methods in the atmospheric sciences. Academic Press, 2nd edition, 2006.
    - +
    - +
    [79]D.S. Wilks. Statistical methods in the atmospheric sciences. Academic Press, 2006. 2nd ed.
    [85]Francis W. Zwiers and Hans von Storch. Taking serial correlation into account in tests of the mean. J. Clim., 8(2):336–351, 1995. doi:10.1175/1520-0442(1995)008<0336:TSCIAI>2.0.CO;2.

    @@ -565,7 +598,7 @@

    Navigation

    \ No newline at end of file