# Net Primary Productivity and the Miami Model

I haven’t been posting for a while as I now realise.
So here a new post about a fairly simple and/but old model to calculate the net primary productivity (NPP), the so called *Miami Model* (Lieth, 1973):

\begin{align}
NPP(T) &= 3000(1+\exp(1.315-0.119 T))

NPP(P) &= 3000 (1-\exp(-0.000664 P))

NPP &= \min(NPP(T),NPP(P))
\end{align}

After reading through the more recent literature, it turns out that the Miami-Model is still regarded as useful proxy for annual NPP.
Global NPP observations are available, for example the Terra/MODIS Net Primary Production Yearly L4 Global 1km.
But these are currently not available as *global* data set.
Instead you can download all tiles (i.e., chunks of 1km by 1km tiles).
I have no idea why, but apparently, nobody is interested in compiling it from the available tile data.
(Maybe a topic for another blog post?).
Anyways, here is what the annual NPP looks like for a present-day climatology, i.e. the Ten Minute Climatology.

Here is a simple Python implementation:

```
import numpy as np
def miami_model(temp,prec,a=3000.,b=1.315,c=0.119,d=0.000664):
npp_temp = a/(1.+np.exp(b-c*temp))
npp_prec = a*(1.-np.exp(-d*prec))
return np.fmin(npp_temp,npp_prec)
```