Dear Mr Ian，<div><span class="Apple-tab-span" style="white-space: pre;"> </span>Firstly, thanks for your patience and suggestion. Recently, I tried to close the salinity budget in a natural model grid at a deep layer without surface forcing but found that the result didn't close even in the magnitude. please let me introduce my works.</div><div> <span class="Apple-tab-span" style="white-space:pre"> </span>First, i chose a tracer cell grid A<font size="2">c</font>(i,j,k)<span style="font-family: -webkit-standard; font-size: medium; text-align: -webkit-center;"> of salinity, which</span><span style="font-family: -webkit-standard; font-size: medium; text-align: -webkit-center;"> is bordered by the lengths </span><span style="font-family: -webkit-standard; font-size: medium; text-align: -webkit-center;"></span><img width="34" height="19" align="MIDDLE" border="0" src="http://mitgcm.org/public/r2_manual/latest/online_documents/img28.png" alt="$ \Delta x_g$" style="font-family: -webkit-standard; text-align: -webkit-center;"><span style="font-family: -webkit-standard; font-size: medium; text-align: -webkit-center;"> and </span><span style="font-family: -webkit-standard; font-size: medium; text-align: -webkit-center;"></span><img width="32" height="19" align="MIDDLE" border="0" src="http://mitgcm.org/public/r2_manual/latest/online_documents/img29.png" alt="$ \Delta y_g$" style="font-family: -webkit-standard; text-align: -webkit-center;"> , and using <span style="font-family: -webkit-standard; font-size: medium;">the forced advection-diffusion equation.</span> </div><div> <img width="199" height="21" align="MIDDLE" border="0" src="http://mitgcm.org/public/r2_manual/latest/online_documents/img902.png" alt="$\displaystyle \partial_t \tau + G_{adv}^\tau = G_{diff}^\tau + G_{forc}^\tau$" style="font-family: -webkit-standard; text-align: -webkit-center; white-space: nowrap;"></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>To calculate advection and diffusive terms, i chose 14 components in different direction around the center of Ac(i,j,k). </div><div><pre><font face="黑体">For the tracer cell there are 6 advective terms, one for each face:(i,j,k denotes 'y','x','z' direction)</font></pre><pre><font face="黑体">2 terms for the 'x' dimension lateral faces: ADVx_SLT, </font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">u(i,j,k) at the west grid and u(i,j+1,k) at the east grid</span><font face="黑体">
2 terms for the 'y' dimension lateral faces: ADVy_SLT, v</font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">(i-1,j,</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">k</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">) at the north grid and v(i,j,k) at the south grid</span></pre><pre><font face="黑体">2 terms for the 'z' dimension bottom faces: ADVr_SLT, </font><font face="黑体">r</font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">(i-1,j,k-1) at the upper grid and r(i,j,k) at the deeper layer</span></pre><pre><font face="黑体">and 8 diffusive terms,</font><span style="font-family: 黑体;">one for each face:(i,j,k denotes 'y','x','z' direction)</span><font face="黑体"><br></font><font face="黑体">
2 terms for the 'x' dimension lateral faces: DFx_SLT, </font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">u(i,j,k) at the west grid and u(i,j+1,k) at the east grid</span><font face="黑体"><br></font><font face="黑体">
2 terms for the 'y dimension lateral faces: DFy_SLT, </font><font face="黑体">v</font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">(i-1,j,</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">k</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">) at the north grid and v(i,j,k) at the south grid</span><font face="黑体"><br></font><font face="黑体">
2 terms for the 'z' dimension bottom faces: DFrE_SLT, </font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">re</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">(i-1,j,k-1) at the upper grid and re(i,j,k) at the deeper layer</span></pre><pre><font face="黑体">2 terms for the 'z' dimension bottom faces: DFrI_SLT, </font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">ri</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">(i-1,j,k-1) at the upper grid and ri(i,j,k) at the deeper layer</span></pre><pre><pre><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;"> In the west-east direction, i calculated the difference between u(i,j+1) and u(i,j)(the eastward </span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">direction</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;"> is positive)</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">as the U.comp of advection terms</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;"> </span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;"> across the salinity </span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">tracer cell grid</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">. S</span><font face="tahoma, verdana, arial, helvetica, sans-serif"><span style="white-space: normal;">imilarly, the north components minus the south one(</span></font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">the northward direction is positive</span><span style="white-space: normal; font-family: tahoma, verdana, arial, helvetica, sans-serif;">), the upper minus the deeper (</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">the upward </span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">direction </span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">is positive). So, i could add 3 Advection terms (multiply by -1)and 4 Diffusive terms together as the right hand terms.</span></pre><pre><font face="tahoma, verdana, arial, helvetica, sans-serif"><span style="white-space: normal;"> Then, in order to fit with the unit of Salinity budget which are in "psi.m^3/month" , the salinity data(Ac(i,j,k)) was multiply by RAC(grid cell area, m^2) and DRC(</span></font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif;">vertical grid spacing, m</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">), and used the "Diff" m.function to get the tendency of salinity term(ds/dt).Likewise, the right hand side was multiply by 3600*24*(28/29/30/31). As a result, the right hand is 10^2 times larger than the left. </span></pre><pre><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;"> Finally, i tried another way to calculate the right hand side , </span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif; white-space: normal;">which is divide by the</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif;"> </span><font face="tahoma, verdana, arial, helvetica, sans-serif">average lengths</font><font face="tahoma, verdana, arial, helvetica, sans-serif"> and their </font><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif;">area</span></pre><pre><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif;"> of the face of</span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif;"> the </span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif;">grid </span><font face="tahoma, verdana, arial, helvetica, sans-serif">cell to be the unit of "psu/month", but it doesn't work!</font></pre></pre></div><div><pre><pre><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif;"><span class="Apple-tab-span" style="white-space:pre"> </span>I hope that you could point out my mistakes and give me some suggestion if you are convenient. </span><span style="font-family: tahoma, verdana, arial, helvetica, sans-serif;">Please forgive my poor work and my unprofessional questions.</span></pre></pre></div><div><span class="Apple-tab-span" style="white-space: pre;"> </span>Thank you for your patient reading! I really appreciate your help! </div><div><br></div><span></span><div>Sincerely,</div><div>Guancheng</div><div><br></div><div><br></div><div><br></div><br><br><br>