Date: 201912
Local time of day: 1201-1800
Location: ZZZ.Airport, CA
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: Personal
Operating under: Part 91
Flight plan: VFR
Mission: Personal
Flight phase: Takeoff / Launch
Airspace: Class D ZZZ
ATC / advisory: Tower ZZZ
Second aircraft: PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Reporter organization: Personal
Reporter function: Pilot Not Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Commercial; Flight Crew Flight Instructor
Human factors: Workload; Communication Breakdown; Situational Awareness
Anomaly: ATC Issue All Types; Conflict NMAC; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Detector: Person Flight Crew
When detected: Other Takeoff
Result: Flight Crew Took Evasive Action
Contributing factors: Staffing; Procedure; Human Factors
Primary problem: Staffing

Narrative: In the afternoon; an airplane reported inbound. The Tower had a hard time understanding the inbound pilot but eventually gave an instruction to 'Cross over the departure end of runway 30; plan to follow a Warrior that is off the departure end'. Note that there was no crossing altitude given to this arriving airplane by the tower controller. This will become critical. The Tower issued a takeoff clearance to our plane from Runway 30 and we were told that the Tower would call the crosswind turn. The arriving airplane descended to 800 feet (local traffic pattern altitude) but was crossing the departure end of the runway exactly where we were departing. We avoided the arriving airplane by about 300 feet vertically. The most disconcerting issue was rather than de-conflict this situation the Tower began to berate the arriving pilot about how they should always cross the airport at 1;200 feet because he was not in a dangerous situation with our departing flight. This conversation went on for at least 20-30 seconds and there was never any communication to us to point out this conflicting traffic.A number of factors played into this near miss. First; the tower staffing situation here at ZZZ has deteriorated. There were at one point in time only 2 controllers. Second; because of the tower staffing issues; the 2 controllers have had to work long hours and work multiple positions simultaneously (tower and ground). This has caused them to be grumpy and argumentative as the stress on them as impacted their ability to deliver safe air traffic services. Third; in this case; the tower controller decided to have a long discussion on the tower frequency about the proper entry procedure rather than ask the pilot to call the tower to have the discussion off frequency. Most importantly; there was in fact no instruction given to the pilot to cross the airport at a specific altitude even though the tower controller went on for quite some length berating the pilot about how they didn't comply when in fact the instruction given to the pilot was ambiguous as not crossing altitude was given. This is an ongoing issue with the tower that hopefully will be resolved by better staffing of the tower before a catastrophic incident occurs.




Synopsis: Flight instructor reported having an NMAC on initial climbout with an aircraft entering the traffic pattern across the departure end of the runway. The instructor stated concerns that inadequate staffing of the tower contributed to the event.