I have been searching for a truly smart web/wifi-based controller. There are products that are close and Rachio is definitely one of the best wifi-based controllers, but unfortunately I have not found my ideal wifi-based controller yet that can match the smartness of my non-wifi/web-based controller with a local weather station.
First, my current timer is a Rainbird ESP-SMTe, which does use the "reservoir" concept you mentioned. It has a local weather station and I like it a lot by the way. I believe the calculation algorithm in the Rainbird (or the so-called "engine") is based on some EPA publications and so the algorithm or engine isn't really proprietary unless the manufacturer drastically deviates from the EPA engine. They generally all take into account common variables such as: soil type, slope, root depth, net application rate, plant type, crop constant Kc (which expresses plant thirstiness), soak cycle length, user selectable % of reference evapo-transpiration rate ETo, sun exposure, zip code (to give reference wind speed and humidity data), daily max/min temperatures, and cumulative rainfall. Max/min temperatures and cumulative rainfall are measured by a weather station that comes with the timer. Note it uses a tipping rain gauge to measure cumulative rainfall instead of just using a rain sensor to sense rain. At the end of each day, water loss through evapo-transpiration (ET) is calculated for each zone based on the input variables. The ET is then subtracted from the reservoir and if the subtraction results in the moisture content falling below a threshold value then a watering session is scheduled. Not all water is retained in the reservoir because of percolation beyond the rootball and not all rainfall reaches the rootball. This really isn't rocket science and the EPA engine is in the public domain.
The ONLY downside with my super smart Rainbird controller is it lacks wifi connection and doesn't use weather forecast information. The reason why it doesn't use weather forecast information is that it's not connected to the web. So its water schedules are always calculating what soil moisture has been depleted due to ET and then catching up to refill the reservoir. This catching up watering strategy instead of a prediction strategy is perfectly fine because the timer is set to water whenever the reservoir moisture level is below some user selectable threshold point. So, assuming all the variables are set correctly for the zone, the Rainbird ESP-SMTe and the reservoir concept will not allow the reservoir to fall too much below some critical point where the plants may wilt and the plants are always properly hydrated without the need for weather forecast.
With the web/wifi-based controllers, they are SUPPOSED TO not only play catch up on the watering (as the Rainbird does) but also to use DAILY weather forecast to modify the watering schedule on the fly. I believe the Rachio does this mostly. Where the Rachio's current algorithm falls short is it doesn't use DAILY temperature forecast to modify the schedules. Its Water Budgeting only modifies the schedules based on weather forecast every week in the latest version. It's almost like season adjustment. The Water Intelligence is used primarily to delay and/or defer watering if rain is predicted, but based on the posts I have read, Water Intelligence doesn't use temperature forecast to modify the schedules on a daily basis. So if the reservoir around the root ball is already close to needing water and Water Intelligence happens to tell the Rachio to skip watering because of rain forecast, everything would be fine as long as the rain forecast is accurate. If the rain forecast is wrong for a few days in a row and if the temperature suddenly warms up (faster than the Rachio's algorithm reacts with its weekly Water Budgeting algorithm), the plants can wilt. I have only been reading the older posts and so possibly the newest software release from Rachio has already taken care of this scenario.
The point I am trying to make with this long post is I want to see wifi-web based controllers such as Rachio to use temperature forecast on a DAILY basis to adjust the watering schedule and to use the reservoir concept. I don't believe the Rachio fully utilizes the reservoir concept. To fully use the reservoir concept, the Rachio will also need to offer a local weather station that can capture CUMULATIVE rainfall data. Generally temperature forecasts are very accurate but rainfall predictions can be wildly off so a local tipping rain gauge is a must with these wifi/web-based controllers. I hope to see Rachio eventually offer a tipping rain gauge and temperature sensor.
Another feature I want to see in an ideal wifi/web-based controller is to allow the master valve to be selectable by zone rather than selectable globally. The master valve can be used to activate fertilizer injectors if it can be set based on zone. Certain zones, such as my Japanese maples, I put on a separate drip irrigation circuit because I don't want to fertilize them. Better, professional models of non-wifi-based controllers have this feature.
I have been doing a lot of research to find the right wifi-based controller that is as smart as my Rainbird but I haven't found it yet, so I am sticking with my Rainbird ESP-SMTe. For the time being I have paired a dumb Orbit controller with wireless remote control with my smart Rainbird controller so that I can use the remote function of the Orbit to control the Rainbird when I need to do maintenance on my drip irrigation system. The Rainbird is the primary controller. The Orbit is set to off and I only use its remote function. I am keeping my eyes open and if/when Rachio improves enough I may well buy one in the future.