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<a href="BTU__Full_8hh.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/* Copyright (C) 2016, 2017, 2019, 2020, 2021, 2022, 2023, 2024 PISM Authors</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> *</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * This file is part of PISM.</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * PISM is free software; you can redistribute it and/or modify it under the</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * terms of the GNU General Public License as published by the Free Software</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> * Foundation; either version 3 of the License, or (at your option) any later</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> * version.</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"> *</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> * PISM is distributed in the hope that it will be useful, but WITHOUT ANY</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> * details.</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> *</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> * You should have received a copy of the GNU General Public License</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> * along with PISM; if not, write to the Free Software</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment"> * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment"> */</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#ifndef BTU_FULL_H</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#define BTU_FULL_H</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "pism/energy/BedThermalUnit.hh"</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "pism/util/Context.hh"</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacepism.html">pism</a> {</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">namespace </span>energy {</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">class </span>BedrockColumn;</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment"></span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">//! @brief Given the temperature of the top of the bedrock, for the duration of one time-step,</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">//! provides upward geothermal flux at that interface at the end of the time-step.</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment"></span><span class="comment">/*!</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment"> The geothermal flux actually applied to the base of an ice sheet is dependent, over time,</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment"> on the temperature of the basal ice itself. The purpose of a bedrock thermal layer</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment"> in an ice sheet model is to implement this dependency by using a physical model</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment"> for the temperature within that layer, the upper lithosphere. Because the</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment"> upper part of the lithosphere stores or releases energy into the ice,</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment"> the typical lithosphere geothermal flux rate is not the same thing as the</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment"> geothermal flux applied to the base of the ice. This issue has long been</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment"> recognized by ice sheet modelers [%e.g. \ref RitzFabreLetreguilly].</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment"></span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment"> For instance, suppose the ice sheet is in a balanced state in which the geothermal</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment"> flux deep in the crust is equal to the heat flux into the ice base. If the</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment"> near-surface ice cools from this state then, because the ice temperature gradient</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment"> is now greater in magnitude, between the warm bedrock and the cooler ice, the ice</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment"> will for some period receive more than the deep geothermal flux rate. Similarly,</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment"> if the ice warms from the balanced state then the temperature difference with</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment"> the bedrock has become smaller and the magnitude of the ice basal heat flux will</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment"> be less than the deep geothermal rate.</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment"></span> </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment"> We regard the lithosphere geothermal flux rate, which is applied in this model</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment"> to the base of the bedrock thermal layer, as a time-independent quantity. This</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment"> concept is the same as in all published ice sheet models, to our knowledge.</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment"></span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment"> Because the relevant layer of bedrock below an ice sheet is typically shallow,</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment"> modeling the bedrock temperature is quite simple.</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment"> Let \f$T_b(t,x,y,z)\f$ be the temperature of the bedrock layer, for elevations</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment"> \f$-L_b \le z \le 0\f$. In this routine, \f$z=0\f$ refers to the top of the</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment"> bedrock, the ice/bedrock interface. (Note \f$z=0\f$ is the base of the ice in</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment"> IceModel, and thus a different location if ice is floating.)</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment"> Let \f$G\f$ be the lithosphere geothermal flux rate, namely the PISM input</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment"> variable `bheatflx`; see Related Page \ref std_names . Let \f$k_b\f$</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment"> = `bedrock_thermal_conductivity` in pism_config.cdl) be the constant thermal</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment"> conductivity of the upper lithosphere. In these terms the actual</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment"> upward heat flux into the ice/bedrock interface is the quantity,</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment"> \f[G_0 = -k_b \frac{\partial T_b}{\partial z}.\f]</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment"> This is the \e output of the method flux_through_top_surface() in this class.</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment"></span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="comment"> The evolution equation solved in this class, for which a timestep is done by the</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="comment"> update() method, is the standard 1D heat equation</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment"> \f[\rho_b c_b \frac{\partial T_b}{\partial t} = k_b \frac{\partial^2 T_b}{\partial z^2}\f]</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment"> where \f$\rho_b\f$ = `bedrock_thermal_density` and \f$c_b\f$ =</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment"> `bedrock_thermal_specific_heat_capacity` in pism_config.cdl.</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment"></span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment"> If 3 or more levels are used then everything is the general case. The lithospheric temperature in</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment"> `temp` is saved in files as `litho_temp`. The flux_through_top_surface() method uses second-order</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment"> differencing to compute the values of \f$G_0\f$.</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment"></span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="comment"> If 2 levels are used then everything is the general case except that flux_through_top_surface()</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment"> method uses first-order differencing to compute the values of \f$G_0\f$.</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment">*/</span></div>
<div class="foldopen" id="foldopen00084" data-start="{" data-end="};">
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full.html"> 84</a></span><span class="keyword">class </span><a class="code hl_class" href="classpism_1_1energy_1_1BTU__Full.html">BTU_Full</a> : <span class="keyword">public</span> <a class="code hl_class" href="classpism_1_1energy_1_1BedThermalUnit.html">BedThermalUnit</a> {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <a class="code hl_class" href="classpism_1_1energy_1_1BTU__Full.html">BTU_Full</a>(std::shared_ptr<const Grid> <a class="code hl_variable" href="namespacepism_a47d754ed3e959d5866b02a1b78b6a5b5.html#a47d754ed3e959d5866b02a1b78b6a5b5">g</a>, <span class="keyword">const</span> <a class="code hl_struct" href="structpism_1_1energy_1_1BTUGrid.html">BTUGrid</a> &vertical_grid);</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full_a70043c844faa8653528ac883a2b61d53.html#a70043c844faa8653528ac883a2b61d53"> 87</a></span> <span class="keyword">virtual</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a70043c844faa8653528ac883a2b61d53.html#a70043c844faa8653528ac883a2b61d53">~BTU_Full</a>() = <span class="keywordflow">default</span>;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment"></span> </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment"> //! Bedrock thermal layer temperature field.</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="comment"></span> <span class="keyword">const</span> <a class="code hl_class" href="classpism_1_1array_1_1Array3D.html">array::Array3D</a>& <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a1be25b6ce9053f7a9346f7bb3c565985.html#a1be25b6ce9053f7a9346f7bb3c565985">temperature</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_ab95d4c0cb1f4a38dfa3a57e822ebc9bb.html#ab95d4c0cb1f4a38dfa3a57e822ebc9bb">bootstrap</a>(<span class="keyword">const</span> <a class="code hl_class" href="classpism_1_1array_1_1Scalar.html">array::Scalar</a> &bedrock_top_temperature);</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_af00d293cc51940cd7bb989ea44c6484c.html#af00d293cc51940cd7bb989ea44c6484c">init_impl</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structpism_1_1InputOptions.html">InputOptions</a> &opts);</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_aaf0477c482f5ffa533b8203a1c3e0fa4.html#aaf0477c482f5ffa533b8203a1c3e0fa4">vertical_spacing_impl</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">virtual</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a8bee6aa46d2a6ebcce317bb2d3970c5a.html#a8bee6aa46d2a6ebcce317bb2d3970c5a">depth_impl</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">virtual</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a3949a4c65419ca66952346efc8047985.html#a3949a4c65419ca66952346efc8047985">Mz_impl</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">virtual</span> <a class="code hl_class" href="classpism_1_1MaxTimestep.html">MaxTimestep</a> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a151903c8f98e0829bdd4b36261fd59e9.html#a151903c8f98e0829bdd4b36261fd59e9">max_timestep_impl</a>(<span class="keywordtype">double</span> my_t) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keyword">using </span><a class="code hl_function" href="classpism_1_1energy_1_1BedThermalUnit_ae1f93a7dbc10618f045c577235b80111.html#ae1f93a7dbc10618f045c577235b80111">BedThermalUnit::update_impl</a>;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a5e8a39408828edfcecd9d23b707048ac.html#a5e8a39408828edfcecd9d23b707048ac">update_impl</a>(<span class="keyword">const</span> <a class="code hl_class" href="classpism_1_1array_1_1Scalar.html">array::Scalar</a> &bedrock_top_temperature,</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordtype">double</span> t, <span class="keywordtype">double</span> dt);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a961a7be0145fc6ad400cb76f6d11a0a7.html#a961a7be0145fc6ad400cb76f6d11a0a7">define_model_state_impl</a>(<span class="keyword">const</span> <a class="code hl_class" href="classpism_1_1File.html">File</a> &output) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a543cf8918b5a9727c5fdac337b3f97d9.html#a543cf8918b5a9727c5fdac337b3f97d9">write_model_state_impl</a>(<span class="keyword">const</span> <a class="code hl_class" href="classpism_1_1File.html">File</a> &output) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="keyword">protected</span>:<span class="comment"></span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="comment"> //! bedrock thermal layer temperature, in kelvin; part of state; uses equally-spaced</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="comment"> //! layers.</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full_a2b9e42164f5f27f66dd78d3419b4e87b.html#a2b9e42164f5f27f66dd78d3419b4e87b"> 112</a></span><span class="comment"></span> std::shared_ptr<array::Array3D> <a class="code hl_variable" href="classpism_1_1energy_1_1BTU__Full_a2b9e42164f5f27f66dd78d3419b4e87b.html#a2b9e42164f5f27f66dd78d3419b4e87b">m_temp</a>;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span><span class="comment"></span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="comment"> //! bedrock thermal conductivity</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full_aff64cb41bb34467c3f3fe180cfb1a7d9.html#aff64cb41bb34467c3f3fe180cfb1a7d9"> 115</a></span><span class="comment"></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="classpism_1_1energy_1_1BTU__Full_aff64cb41bb34467c3f3fe180cfb1a7d9.html#aff64cb41bb34467c3f3fe180cfb1a7d9">m_k</a>;<span class="comment"></span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="comment"> //! diffusivity of the heat flow within the bedrock layer</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full_aeccb73d2035ccae775fca3b19d9ef89c.html#aeccb73d2035ccae775fca3b19d9ef89c"> 117</a></span><span class="comment"></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="classpism_1_1energy_1_1BTU__Full_aeccb73d2035ccae775fca3b19d9ef89c.html#aeccb73d2035ccae775fca3b19d9ef89c">m_D</a>;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment"></span> </div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment"> //! number of vertical levels within the bedrock</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full_a1dff2088600230d126f26d7254332a44.html#a1dff2088600230d126f26d7254332a44"> 120</a></span><span class="comment"></span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="classpism_1_1energy_1_1BTU__Full_a1dff2088600230d126f26d7254332a44.html#a1dff2088600230d126f26d7254332a44">m_Mbz</a>;<span class="comment"></span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment"> //! thickness of the bedrock layer, in meters</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full_a3cc895e82591494e61e5ab0b32c8c5a1.html#a3cc895e82591494e61e5ab0b32c8c5a1"> 122</a></span><span class="comment"></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="classpism_1_1energy_1_1BTU__Full_a3cc895e82591494e61e5ab0b32c8c5a1.html#a3cc895e82591494e61e5ab0b32c8c5a1">m_Lbz</a>;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="comment"></span> </div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment"> //! true if the model needs to "bootstrap" the temperature field during the first time step</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full_a81d03b90bdc35987d1c9fbb17f3d6503.html#a81d03b90bdc35987d1c9fbb17f3d6503"> 125</a></span><span class="comment"></span> <span class="keywordtype">bool</span> <a class="code hl_variable" href="classpism_1_1energy_1_1BTU__Full_a81d03b90bdc35987d1c9fbb17f3d6503.html#a81d03b90bdc35987d1c9fbb17f3d6503">m_bootstrapping_needed</a>;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classpism_1_1energy_1_1BTU__Full_a2374e15fd50a204be73943c1811fa703.html#a2374e15fd50a204be73943c1811fa703">update_flux_through_top_surface</a>();</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"><a class="line" href="classpism_1_1energy_1_1BTU__Full_a7a36bb90d613f2df622e1aff5136866f.html#a7a36bb90d613f2df622e1aff5136866f"> 129</a></span> std::shared_ptr<BedrockColumn> <a class="code hl_variable" href="classpism_1_1energy_1_1BTU__Full_a7a36bb90d613f2df622e1aff5136866f.html#a7a36bb90d613f2df622e1aff5136866f">m_column</a>;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>};</div>
</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span>} <span class="comment">// end of namespace energy</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span>} <span class="comment">// end of namespace pism</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> </div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="preprocessor">#endif </span><span class="comment">/* BTU_FULL_H */</span><span class="preprocessor"></span></div>
<div class="ttc" id="aclasspism_1_1File_html"><div class="ttname"><a href="classpism_1_1File.html">pism::File</a></div><div class="ttdoc">High-level PISM I/O class.</div><div class="ttdef"><b>Definition</b> <a href="File_8hh_source.html#l00054">File.hh:55</a></div></div>
<div class="ttc" id="aclasspism_1_1MaxTimestep_html"><div class="ttname"><a href="classpism_1_1MaxTimestep.html">pism::MaxTimestep</a></div><div class="ttdoc">Combines the max. time step with the flag indicating if a restriction is active. Makes is possible to...</div><div class="ttdef"><b>Definition</b> <a href="MaxTimestep_8hh_source.html#l00031">MaxTimestep.hh:31</a></div></div>
<div class="ttc" id="aclasspism_1_1array_1_1Array3D_html"><div class="ttname"><a href="classpism_1_1array_1_1Array3D.html">pism::array::Array3D</a></div><div class="ttdoc">A virtual class collecting methods common to ice and bedrock 3D fields.</div><div class="ttdef"><b>Definition</b> <a href="Array3D_8hh_source.html#l00033">Array3D.hh:33</a></div></div>
<div class="ttc" id="aclasspism_1_1array_1_1Scalar_html"><div class="ttname"><a href="classpism_1_1array_1_1Scalar.html">pism::array::Scalar</a></div><div class="ttdef"><b>Definition</b> <a href="Scalar_8hh_source.html#l00031">Scalar.hh:31</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a151903c8f98e0829bdd4b36261fd59e9_html_a151903c8f98e0829bdd4b36261fd59e9"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a151903c8f98e0829bdd4b36261fd59e9.html#a151903c8f98e0829bdd4b36261fd59e9">pism::energy::BTU_Full::max_timestep_impl</a></div><div class="ttdeci">virtual MaxTimestep max_timestep_impl(double my_t) const</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00147">BTU_Full.cc:147</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a1be25b6ce9053f7a9346f7bb3c565985_html_a1be25b6ce9053f7a9346f7bb3c565985"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a1be25b6ce9053f7a9346f7bb3c565985.html#a1be25b6ce9053f7a9346f7bb3c565985">pism::energy::BTU_Full::temperature</a></div><div class="ttdeci">const array::Array3D & temperature() const</div><div class="ttdoc">Bedrock thermal layer temperature field.</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00243">BTU_Full.cc:243</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a1dff2088600230d126f26d7254332a44_html_a1dff2088600230d126f26d7254332a44"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a1dff2088600230d126f26d7254332a44.html#a1dff2088600230d126f26d7254332a44">pism::energy::BTU_Full::m_Mbz</a></div><div class="ttdeci">unsigned int m_Mbz</div><div class="ttdoc">number of vertical levels within the bedrock</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8hh_source.html#l00120">BTU_Full.hh:120</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a2374e15fd50a204be73943c1811fa703_html_a2374e15fd50a204be73943c1811fa703"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a2374e15fd50a204be73943c1811fa703.html#a2374e15fd50a204be73943c1811fa703">pism::energy::BTU_Full::update_flux_through_top_surface</a></div><div class="ttdeci">void update_flux_through_top_surface()</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00210">BTU_Full.cc:210</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a2b9e42164f5f27f66dd78d3419b4e87b_html_a2b9e42164f5f27f66dd78d3419b4e87b"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a2b9e42164f5f27f66dd78d3419b4e87b.html#a2b9e42164f5f27f66dd78d3419b4e87b">pism::energy::BTU_Full::m_temp</a></div><div class="ttdeci">std::shared_ptr< array::Array3D > m_temp</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8hh_source.html#l00112">BTU_Full.hh:112</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a3949a4c65419ca66952346efc8047985_html_a3949a4c65419ca66952346efc8047985"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a3949a4c65419ca66952346efc8047985.html#a3949a4c65419ca66952346efc8047985">pism::energy::BTU_Full::Mz_impl</a></div><div class="ttdeci">virtual unsigned int Mz_impl() const</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00128">BTU_Full.cc:128</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a3cc895e82591494e61e5ab0b32c8c5a1_html_a3cc895e82591494e61e5ab0b32c8c5a1"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a3cc895e82591494e61e5ab0b32c8c5a1.html#a3cc895e82591494e61e5ab0b32c8c5a1">pism::energy::BTU_Full::m_Lbz</a></div><div class="ttdeci">double m_Lbz</div><div class="ttdoc">thickness of the bedrock layer, in meters</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8hh_source.html#l00122">BTU_Full.hh:122</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a543cf8918b5a9727c5fdac337b3f97d9_html_a543cf8918b5a9727c5fdac337b3f97d9"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a543cf8918b5a9727c5fdac337b3f97d9.html#a543cf8918b5a9727c5fdac337b3f97d9">pism::energy::BTU_Full::write_model_state_impl</a></div><div class="ttdeci">virtual void write_model_state_impl(const File &output) const</div><div class="ttdoc">The default (empty implementation).</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00142">BTU_Full.cc:142</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a5e8a39408828edfcecd9d23b707048ac_html_a5e8a39408828edfcecd9d23b707048ac"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a5e8a39408828edfcecd9d23b707048ac.html#a5e8a39408828edfcecd9d23b707048ac">pism::energy::BTU_Full::update_impl</a></div><div class="ttdeci">virtual void update_impl(const array::Scalar &bedrock_top_temperature, double t, double dt)</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00156">BTU_Full.cc:156</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a70043c844faa8653528ac883a2b61d53_html_a70043c844faa8653528ac883a2b61d53"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a70043c844faa8653528ac883a2b61d53.html#a70043c844faa8653528ac883a2b61d53">pism::energy::BTU_Full::~BTU_Full</a></div><div class="ttdeci">virtual ~BTU_Full()=default</div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a7a36bb90d613f2df622e1aff5136866f_html_a7a36bb90d613f2df622e1aff5136866f"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a7a36bb90d613f2df622e1aff5136866f.html#a7a36bb90d613f2df622e1aff5136866f">pism::energy::BTU_Full::m_column</a></div><div class="ttdeci">std::shared_ptr< BedrockColumn > m_column</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8hh_source.html#l00129">BTU_Full.hh:129</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a81d03b90bdc35987d1c9fbb17f3d6503_html_a81d03b90bdc35987d1c9fbb17f3d6503"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a81d03b90bdc35987d1c9fbb17f3d6503.html#a81d03b90bdc35987d1c9fbb17f3d6503">pism::energy::BTU_Full::m_bootstrapping_needed</a></div><div class="ttdeci">bool m_bootstrapping_needed</div><div class="ttdoc">true if the model needs to "bootstrap" the temperature field during the first time step</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8hh_source.html#l00125">BTU_Full.hh:125</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a8bee6aa46d2a6ebcce317bb2d3970c5a_html_a8bee6aa46d2a6ebcce317bb2d3970c5a"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a8bee6aa46d2a6ebcce317bb2d3970c5a.html#a8bee6aa46d2a6ebcce317bb2d3970c5a">pism::energy::BTU_Full::depth_impl</a></div><div class="ttdeci">virtual double depth_impl() const</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00133">BTU_Full.cc:133</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_a961a7be0145fc6ad400cb76f6d11a0a7_html_a961a7be0145fc6ad400cb76f6d11a0a7"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_a961a7be0145fc6ad400cb76f6d11a0a7.html#a961a7be0145fc6ad400cb76f6d11a0a7">pism::energy::BTU_Full::define_model_state_impl</a></div><div class="ttdeci">virtual void define_model_state_impl(const File &output) const</div><div class="ttdoc">The default (empty implementation).</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00137">BTU_Full.cc:137</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_aaf0477c482f5ffa533b8203a1c3e0fa4_html_aaf0477c482f5ffa533b8203a1c3e0fa4"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_aaf0477c482f5ffa533b8203a1c3e0fa4.html#aaf0477c482f5ffa533b8203a1c3e0fa4">pism::energy::BTU_Full::vertical_spacing_impl</a></div><div class="ttdeci">virtual double vertical_spacing_impl() const</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00124">BTU_Full.cc:124</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_ab95d4c0cb1f4a38dfa3a57e822ebc9bb_html_ab95d4c0cb1f4a38dfa3a57e822ebc9bb"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_ab95d4c0cb1f4a38dfa3a57e822ebc9bb.html#ab95d4c0cb1f4a38dfa3a57e822ebc9bb">pism::energy::BTU_Full::bootstrap</a></div><div class="ttdeci">virtual void bootstrap(const array::Scalar &bedrock_top_temperature)</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00251">BTU_Full.cc:251</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_aeccb73d2035ccae775fca3b19d9ef89c_html_aeccb73d2035ccae775fca3b19d9ef89c"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_aeccb73d2035ccae775fca3b19d9ef89c.html#aeccb73d2035ccae775fca3b19d9ef89c">pism::energy::BTU_Full::m_D</a></div><div class="ttdeci">double m_D</div><div class="ttdoc">diffusivity of the heat flow within the bedrock layer</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8hh_source.html#l00117">BTU_Full.hh:117</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_af00d293cc51940cd7bb989ea44c6484c_html_af00d293cc51940cd7bb989ea44c6484c"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_af00d293cc51940cd7bb989ea44c6484c.html#af00d293cc51940cd7bb989ea44c6484c">pism::energy::BTU_Full::init_impl</a></div><div class="ttdeci">virtual void init_impl(const InputOptions &opts)</div><div class="ttdoc">Initialize the bedrock thermal unit.</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8cc_source.html#l00087">BTU_Full.cc:87</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_aff64cb41bb34467c3f3fe180cfb1a7d9_html_aff64cb41bb34467c3f3fe180cfb1a7d9"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full_aff64cb41bb34467c3f3fe180cfb1a7d9.html#aff64cb41bb34467c3f3fe180cfb1a7d9">pism::energy::BTU_Full::m_k</a></div><div class="ttdeci">double m_k</div><div class="ttdoc">bedrock thermal conductivity</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8hh_source.html#l00115">BTU_Full.hh:115</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BTU__Full_html"><div class="ttname"><a href="classpism_1_1energy_1_1BTU__Full.html">pism::energy::BTU_Full</a></div><div class="ttdoc">Given the temperature of the top of the bedrock, for the duration of one time-step,...</div><div class="ttdef"><b>Definition</b> <a href="BTU__Full_8hh_source.html#l00084">BTU_Full.hh:84</a></div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BedThermalUnit_ae1f93a7dbc10618f045c577235b80111_html_ae1f93a7dbc10618f045c577235b80111"><div class="ttname"><a href="classpism_1_1energy_1_1BedThermalUnit_ae1f93a7dbc10618f045c577235b80111.html#ae1f93a7dbc10618f045c577235b80111">pism::energy::BedThermalUnit::update_impl</a></div><div class="ttdeci">virtual void update_impl(const array::Scalar &bedrock_top_temperature, double t, double dt)=0</div></div>
<div class="ttc" id="aclasspism_1_1energy_1_1BedThermalUnit_html"><div class="ttname"><a href="classpism_1_1energy_1_1BedThermalUnit.html">pism::energy::BedThermalUnit</a></div><div class="ttdoc">Given the temperature of the top of the bedrock, for the duration of one time-step,...</div><div class="ttdef"><b>Definition</b> <a href="BedThermalUnit_8hh_source.html#l00101">BedThermalUnit.hh:101</a></div></div>
<div class="ttc" id="anamespacepism_a47d754ed3e959d5866b02a1b78b6a5b5_html_a47d754ed3e959d5866b02a1b78b6a5b5"><div class="ttname"><a href="namespacepism_a47d754ed3e959d5866b02a1b78b6a5b5.html#a47d754ed3e959d5866b02a1b78b6a5b5">pism::g</a></div><div class="ttdeci">static const double g</div><div class="ttdef"><b>Definition</b> <a href="exactTestP_8cc_source.html#l00036">exactTestP.cc:36</a></div></div>
<div class="ttc" id="anamespacepism_html"><div class="ttname"><a href="namespacepism.html">pism</a></div><div class="ttdef"><b>Definition</b> <a href="AgeColumnSystem_8cc_source.html#l00023">AgeColumnSystem.cc:23</a></div></div>
<div class="ttc" id="astructpism_1_1InputOptions_html"><div class="ttname"><a href="structpism_1_1InputOptions.html">pism::InputOptions</a></div><div class="ttdef"><b>Definition</b> <a href="Component_8hh_source.html#l00058">Component.hh:58</a></div></div>
<div class="ttc" id="astructpism_1_1energy_1_1BTUGrid_html"><div class="ttname"><a href="structpism_1_1energy_1_1BTUGrid.html">pism::energy::BTUGrid</a></div><div class="ttdef"><b>Definition</b> <a href="BedThermalUnit_8hh_source.html#l00036">BedThermalUnit.hh:36</a></div></div>
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