# Modeling the total water inflow across multiple reservoirs

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.

• Thank you for your inputs. At this point, I'm planning to do the analysis river by river, which allows me to estimate a distribution of daily inflow given certain variables (I don't have elevation, but only precipitation, and temperature. Acceleration should be captured by some lag variables of inflow, right?). Then, if there's not a lot of cross-sectional correlation across rivers, I can compute the joint distribution of the daily inflows to the firm by convoluting the marginal distribution of each river. Would that work? – Andrew Apr 1 at 7:54
• I don't know how but I could have deleted some comments by mistake. sorry – Andrew Apr 1 at 8:21
• You haven't, i have deleted them, because i feared questions and a resulting discussion in the remarks. A few months ago i have dabbled with terrain modelling based on hydrology but yielded when it came to the math of differentiation and integration. There is much information out there on modelling of hydrology, younger then 2000. – user20217 Apr 4 at 11:03
• Unfortunately, I don't have access to elevation info, but only the inflow. So I was thinking of modeling in some AR(p) process. The literature is huge. Any good ref? – Andrew Apr 4 at 11:34
• Due to a lack of imagination, i have no idea how to model a directional flow without surface data, elevation, slope, transport capacity and area of watersheds and tributaries. – user20217 Apr 4 at 11:41