Date: 201909
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: IMC
Light: Night
Aircraft: EMB ERJ 145 ER/LR
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class C ZZZ
ATC / advisory: TRACON ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Confusion; Communication Breakdown
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR; Inflight Event / Encounter Weather / Turbulence
Detector: Person Flight Crew
When detected: In-flight
Result: General None Reported / Taken
Contributing factors: Procedure; Weather; Human Factors
Primary problem: Ambiguous

Narrative: Dispatch had and sent us a release showing a new TAF in the non-planning weather section. The two lines that applied were: 0047Z 12009KT 3/4SM BR OVC002; 0300Z 14005KT 1/2SM FG OVC003 WS020/22035KT. The weather was stable; non-convective; [and] restricted visibility due to lake fog and mist. Past two METARS obtained via aviationweather.gov METAR history showed visibility consistently holding at 3/4SM and 6000 RVR; TWR VIS 1SM. Our planned ETA to the runway; not gate; was scheduled to be at XA54Z; prior to XB00Z forecast.My First Officer and I discussed and agreed that we were legal to depart; because we were set to arrive prior to forecasted lower weather. In addition; other weather reports indicated that the visibility had remained consistent with required minimums for the planned GPS approach. The First Officer and I also discussed the shorter taxi out and routing we were expecting due to the traffic volume; which would allow us to arrive even earlier than planned ETA. With no contact from Dispatch concerning the weather; the First Officer and I agreed that release to the ZZZ1 airport with current combination of weather reports; in accordance with [the Flight Operations Manual]; was safe and legal.On the takeoff roll; we received an ACARS message that I told my First Officer to disregard until we were airborne; because we were in the middle of the takeoff roll. Once airborne at a safe altitude; FO (First Officer) checked the message and it read 'Captain Call Me; Weather in ZZZ1.' I handed off the aircraft controls to my FO and began to message my Dispatcher. Dispatch was concerned that our time of arrival to the gate was in forecasted weather that was below approach minimums. I informed him via ACARS of what my FO and I discussed; that our ETA to the runway was prior to the TAF line; and in addition actual ETA was showing about 30 minutes earlier than planned. Dispatcher and I agreed that with our actual ETA and consistent METAR reports; that the flight could continue safely.As we were crossing the initial approach fix for the GPS; Approach Control reported visibility dropped to 1/4 SM and 2500 RVR. I requested to cancel approach clearance and hold as published at an intermediate approach fix. We figured out that we had about an hour of holding fuel before having to divert to our original alternate of ZZZ2. The visibility RVR changed multiple times; but the lowest of the reports were still showing less than 4000 RVR. I made the decision to continue holding until the lowest RVR reported required visibility. At this time; after standard communication during holding; Dispatch instructed us to change our alternate airport to ZZZ. That reduced our holding time from 60 minutes to 20 minutes. The FO and I decided to immediately divert back to ZZZ given the new fuel numbers. We needed minimum 4;600 LBS of fuel to get back to ZZZ with a ZZZ3 alternate initially; we began the diversion at 5;100 LBS of fuel. Due to weather changing in ZZZ; Dispatch changed our alternate to ZZZ from ZZZ3 to ZZZ4; which increased the alternate fuel needed. Due to routing and the change of alternates again; I had to declare minimum fuel with Chicago Center. I tried to work with Dispatch to get us a closer alternate; but Dispatch said he couldn't; that we should divert to ZZZ4 for fuel. We diverted to ZZZ4 for fueling. Then departed back to ZZZ with no further incident.Upon landing I was asked to call the Supervisor. He inquired on the Dispatcher's communication with me prior to departure. I told the Supervisor that the first communication we received had been during the takeoff roll. We discussed a few other details about the evening's events; but primarily whether or not the Dispatcher contacted me prior to the takeoff roll. This concluded the event. I'm not entirely sure how to chalk this one up. Maybe Dispatcher workload. My FO and I; given our scheduled ETA to the runway; not the gate; current weather reports; actual anticipated ETA; along with our experience with lake fog and similar visibility conditions; agreed we were both legal and safe to depart. Normally dispatchers will call me or lock out the flight release for me to call them about a weather situation. When the Dispatcher signed the release; I believed he agreed with what my FO and I were seeing. This event; in my opinion; was never in question in terms of legality or safety.Working on a more standardized dispatch methodology for weather coordination. In the past I have had dispatchers lock me out of a flight release; so I could call them and discuss weather. Also a standardized go no-go decision making for Dispatch would be helpful for flight crews. Last week; I had a Dispatcher trying to make me fly an aircraft in violent thunderstorms; low visibility in extreme precipitation; variable winds gusting up to 35 kts; all on a planned runway of 6;700 feet. I made the decision to defer that flight; which resulted in a cancellation. I also have had similar experiences in the past where I had to tell the Dispatcher I was not departing unless I knew I had a good chance of actually making it in to the planned arrival airport. There seems to be inconsistencies between dispatchers when it comes to dispatching flights to airports with weather.Other Dispatch issues - Dispatch signed release. Flight crew agreed; flight ETA was in TAF line that supported GPS minimums. Dispatcher did not send message concerning weather until flight crew was in takeoff roll. Dispatch did not contact us with his concerns about the weather until we were on our takeoff roll. I had discussed and agreed with my crew that our flights ETA was legally in the TAF line that supported approach minimums.




Synopsis: EMB-145 Captain reported receiving conflicting and delayed messages from Dispatch concerning safe enroute weather and alternates.