I'm new to hydrology and I have a question regarding the modeling of multiple reservoirs. I need to estimate the total water inflow to multiple reservoirs that will be observed tomorrow, conditional on the water inflow, temperatures and rainfalls in each reservoir today. What I have in mind is a model similar to
$$ TotalInflow_{t} = \beta_0 + \sum_i \beta_i \cdot Inflow_{it-1} + \sum_i \gamma_i \cdot Temperature_{it-1} + \sum_i \phi_i \cdot Rainfall_{it-1} + \epsilon_t,$$
where $i$ denotes each single reservoirs, $t$ denotes time and $\epsilon_t$ is a random error. Of course, I plan to augment this simple model with lags variables and fixed effects. Importantly, the reservoirs in my data are not connected (e.g., a company owns multiple dams in different rivers). However, looking into the hydrology literature, I could only find paper dealing with a single reservoir rather than the sum of the total inflows across multiple reservoirs (e.g., Coulibalya et al., 2000). What is the common approach in hydrology for this problem (e.g., ARMA models? How many lags? Differencing?)? Do you have a specific reference?
Bibliography: Coulibaly, Paulin, François Anctil, and Bernard Bobée. "Daily reservoir inflow forecasting using artificial neural networks with stopped training approach." Journal of Hydrology 230, no. 3-4 (2000): 244-257.
