# Estimating Global Gross Primary Production Using an Improved MODIS Leaf Area Index Dataset
## Appendix A The Structure of the Model
### Photosynthesis of Nitrogen Content
The leaf nitrogen concentration (\(N_{a}\)) is a function of the C/N ratio and specific leaf area, which is expressed as follows:  
\[N_{a}=\frac{1}{CN_{l}\times SLA} \tag{20}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & **Site ID** & **Latitude** & **Longitude** & **Period** & **RRMSE** \\ \hline DNF & RU-SkP & 62.255 & 129.168 & 2012–2014 & 1.1955 \\ EBF & AU-Whr & \(-36.6732\) & 145.0294 & 2012–2014 & 0.4912 \\ EBF & CN-Din & 23.1733 & 112.5361 & 2005–2003 & 0.5219 \\ EBF & GH-Ark & 5.2685 & \(-2.6942\) & 2011–2012 & 0.4864 \\ EBF & AU-Wac & \(-37.4259\) & 145.1878 & 2005–2008 & 0.1021 \\ EBF & AU-Tum & \(-35.6566\) & 148.1517 & 2001–2014 & 0.9606 \\ EBF & AU-Wom & \(-37.4222\) & 144.0944 & 2010–2014 & 0.4957 \\ EBF & AU-Cum & \(-33.6152\) & 150.7236 & 2012–2014 & 0.9677 \\ EBF & FR-Pue & 43.7413 & 3.5957 & 2001–2014 & 0.4651 \\ ENF & US-Me5 & \(44.4372\) & \(-121.5668\) & 2000–2002 & 0.4521 \\ ENF & FF-Sod & \(67.3624\) & \(26.6386\) & 2001–2014 & 0.4508 \\ ENF & FI-Let & \(60.6418\) & 23.9595 & 2010–2012 & 0.5982 \\ ENF & FI-Hyy & \(61.8474\) & 24.2948 & 2000–2014 & 0.6253 \\ ENF & FR-LBr & \(44.7171\) & \(-0.7693\) & 2000–2008 & 0.6623 \\ ENF & US-Me6 & \(44.3233\) & \(-121.6078\) & 2011–2014 & 0.2973 \\ ENF & US-Prr & \(65.1237\) & \(-147.4876\) & 2010–2014 & 0.3164 \\ ENF & US-Me3 & \(44.3154\) & \(-121.6078\) & 2004–2008 & 0.1513 \\ ENF & NL-Loo & \(52.1666\) & \(5.7436\) & 2000–2014 & 0.1057 \\ ENF & IT-Ren & \(46.5869\) & \(11.4337\) & 2005–2013 & 0.9499 \\ ENF & RU-Fyo & \(56.4615\) & \(32.9221\) & 2000–2014 & 0.0590 \\ ENF & US-Blo & \(38.8953\) & \(-120.6328\) & 2000–2007 & 1.5783 \\ ENF & IT-La2 & \(45.9542\) & \(11.2853\) & 2001–2001 & 0.6657 \\ ENF & US-Wi4 & \(46.7393\) & \(-91.1663\) & 2002–2005 & 0.0204 \\ ENF & US-Me2 & \(44.4523\) & \(-121.5574\) & 2002–2014 & 0.0919 \\ ENF & IT-Lav & \(45.9562\) & \(11.2813\) & 2003–2014 & 0.6185 \\ ENF & US-GLE & \(41.3665\) & \(-106.2399\) & 2005–2014 & 0.2307 \\ ENF & CN-Qia & \(26.7414\) & \(115.0581\) & 2003–2005 & 0.2926 \\ ENF & DE-Tha & \(50.9626\) & \(13.5651\) & 2000–2014 & 0.5088 \\ ENF & CA-NS3 & \(55.9117\) & \(-98.3822\) & 2001–2005 & 0.4440 \\ ENF & US-NR1 & \(40.0329\) & \(-105.5464\) & 2000–2014 & 0.3379 \\ ENF & CA-SF2 & \(54.2539\) & \(-105.8775\) & 2003–2004 & 0.7883 \\ ENF & CA-SF1 & \(54.485\) & \(-105.8176\) & 2004–2005 & 0.7912 \\ ENF & CA-NS2 & \(55.9058\) & \(-98.5247\) & 2001–2004 & 0.5028 \\ ENF & CA-NS4 & \(55.9144\) & \(-98.3806\) & 2002–2005 & 0.7572 \\ ENF & CZ-RR1 & \(49.5021\) & \(18.5369\) & 2004–2014 & 0.2705 \\ ENF & CA-Man & \(55.8796\) & \(-98.4808\) & 2000–2004 & 0.5992 \\ ENF & CA-Qfo & \(49.6925\) & \(-74.3421\) & 2004–2010 & 0.7685 \\ ENF & DE-Lkb & \(49.0996\) & \(13.3047\) & 2009–2013 & 0.5555 \\ ENF & CA-NS5 & \(58.6831\) & \(-98.4858\) & 2002–2005 & 0.7947 \\ ENF & CA-NS1 & \(55.8792\) & \(-98.4839\) & 2002–2005 & 0.7684 \\ GRA & AT-Neu & \(47.1167\) & \(11.3175\) & 2002–2012 & 0.9405 \\ GRA & US-ARI & \(36.4267\) & \(-99.42\) & 2009–2012 & 1.4371 \\ GRA & US-Wkg & \(31.7365\) & \(-109.9419\) & 2006–2014 & 0.1482 \\ GRA & RU-TKs & \(128.8878\) & 2012–2014 & 0.1329 \\ GRA & US-AR2 & \(36.6358\) & \(-99.5975\) & \(2010–2011\) & 0.1587 \\ GRA & RU-Hal & \(54.7252\) & \(90.0022\) & 2003–2004 & 0.1047 \\ GRA & PA-SPs & \(9.3138\) & \(-79.6314\) & 2007–2009 & 0.0382 \\ GRA & US-Goo & \(34.2547\) & \(-89.8735\) & 2003–2006 & 0.2912 \\ GRA & CH-Cha & \(47.2102\) & \(8.4104\) & 2005–2014 & 0.8429 \\ GRA & DE-RuR & \(50.6219\) & \(6.3041\) & 2012–2014 & 0.3521 \\ GRA & CH-Oe1 & \(47.2858\) & \(7.7319\) & 2002–2008 & 0.5104 \\ GRA & AU-Yrnc & \(-34.9893\) & \(146.2907\) & 2013–2013 & 0.1063 \\ GRA & US-SRG & \(31.7894\) & \(-110.8277\) & 2008–2014 & 0.2094 \\ GRA & DE-Gri & \(50.95\) & \(13.5126\) & 2004–2011 & 0.4390 \\ GRA & CZ-BK2 & \(49.4944\) & \(18.5429\) & 2006–2012 & 0.3105 \\ GRA & CH-Fru & \(47.1158\) & \(8.5378\) & 2010–2014 & 1.9716 \\ GRA & CN-Du2 & \(42.0467\) & \(116.2836\) & 2007–2008 & 0.1365 \\ GRA & IT-MBo & \(46.0147\) & \(11.0458\) & 2003–2013 & 0.6747 \\ GRA & CN-Cng & \(44.5934\) & \(123.5092\) & 2007–2010 & 0.5325 \\ GRA & AU-DaP & \(-14.0633\) & \(131.3181\) & 2007–2013 & 0.9532 \\ GRA & CN-HaM & \(37.37\) &