1.what are the connections between the terrestrial water balance and the terrestrial energy balance?

Both term are included in the heat budget system of planet.

Explanation:

As the Earth has a terrestrial heat energy budget similarly, the water also exhibits the same balance in connection to the landmass.  The global balance is maintained through the transfer of excessive heat from the lower layer to the upper layers.  Such as from polar region to tropics and tropics to polar region and this cycle repeats itself and hence balancing the deficit that exists from north to south.  As the incoming solar energy gained at the surface the heat energy spreads over the landscape in the form of positively charged electrons and this energy spreads and heats the landmass which then further disphades into the oceans and seas, lakes and other water bodies.  Apart from this the heat energy that falls over the oceans directly, some of it gets stored and some evaporates while the other precipitated over landmass hence cooling it and recharging the aquifers. This infiltration in the ground creates a balance between the amount of energy radiated in the terrestrial surface and water balance.

Answerland;

There is no map, maybe give the link, it may be b