NOTE, THIS IS A PARTIAL AND INCOMPLETE ANSWER.
First step, lets give a letter to each area (we have 30 areas, so we need to be case-sensitive):
$$ \begin{array}{cccccccccccc} z & z & z & C & A & A & D & D & D & D & B & B \\ y & z & C & C & C & A & w & w & B & B & B & v \\ y & z & z & u & A & A & w & x & x & B & v & v \\ u & u & u & u & s & w & w & t & x & x & x & v \\ u & r & u & s & s & s & s & t & t & p & p & v \\ r & r & r & r & s & n & m & m & t & t & p & q \\ r & j & j & n & n & n & m & o & o & p & p & q \\ k & j & l & n & l & m & m & m & o & o & p & q \\ k & j & l & l & l & g & c & m & h & i & i & i \\ j & j & f & f & f & g & c & c & h & h & e & i \\ a & f & f & b & g & g & g & c & h & e & e & i \\ a & a & a & b & b & b & b & c & d & d & e & e \\ \end{array}$$
Now, lets number each one accordingly to its water-level:
$$ \begin{array}{cccccccccccc} z_3 & z_3 & z_3 & C_2 & A_3 & A_3 & D_1 & D_1 & D_1 & D_1 & B_3 & B_3 \\ y_2 & z_2 & C_1 & C_1 & C_1 & A_2 & w_3 & w_3 & B_2 & B_2 & B_2 & v_4 \\ y_1 & z_1 & z_1 & u_3 & A_1 & A_1 & w_2 & x_2 & x_2 & B_1 & v_3 & v_3 \\ u_2 & u_2 & u_2 & u_2 & s_3 & w_1 & w_1 & t_3 & x_1 & x_1 & x_1 & v_2 \\ u_{1a} & r_3 & u_{1b} & s_2 & s_2 & s_2 & s_2 & t_2 & t_2 & p_4 & p_4 & v_1 \\ r_2 & r_2 & r_2 & r_2 & s_1 & n_3 & m_4 & m_4 & t_1 & t_1 & p_3 & q_3 \\ r_1 & j_4 & j_4 & n_2 & n_2 & n_2 & m_3 & o_2 & o_2 & p_2 & p_2 & q_2 \\ k_2 & j_3 & l_2 & n_1 & l_2 & m_2 & m_2 & m_2 & o_1 & o_1 & p_1 & q_1 \\ k_1 & j_2 & l_1 & l_1 & l_1 & g_3 & c_4 & m_1 & h_3 & i_3 & i_3 & i_3 \\ j_1 & j_1 & f_2 & f_2 & f_2 & g_2 & c_3 & c_3 & h_2 & h_2 & e_3 & i_2 \\ a_2 & f_1 & f_1 & b_2 & g_1 & g_1 & g_1 & c_2 & h_1 & e_2 & e_2 & i_1 \\ a_1 & a_1 & a_1 & b_1 & b_1 & b_1 & b_1 & c_1 & d_1 & d_1 & e_1 & e_1 \\ \end{array}$$
Now, we take every different symbol as a variable. We can reduce this to a boolean formula with 83 variables: $a_1, a_2, b_1, b_2, c_1, c_2, c_3, c_4, d_1, e_1, e_2, e_3, f_1, f_2, g_1, g_2, g_3, h_1, h_2, h_3, i_1, i_2, i_3, j_1, j_2, j_3, j_4, k_1, k_2, l_1, l_2, m_1, m_2, m_3, m_4, n_1, n_2, n_3, o_1, o_2, p_1, p_2, p_3, p_4, q_1, q_2, q_3, r_1, r_2, r_3, s_1, s_2, s_3, t_1, t_2, t_3, u_{1a}, u_{1b}, u_2, u_3, v_1, v_2, v_3, v_4, w_1, w_2, w_3, x_1, x_2, y_1, y_2, z_1, z_2, z_3, A_1, A_2, A_3, B_1, B_2, B_3, C_1, C_2, D_1$
Lets mount the formula. First the gravity constraints, they have the format $(\delta_{i+1} \to \delta_i)$, which can be simplified to $(\lnot\delta_{i+1} \lor \delta_i)$. We have 53 gravity constraints:
$$ \begin{array}{cccccccccc} (\lnot a_2 \lor a_1) & \land & (\lnot b_2 \lor b_1) & \land & (\lnot c_2 \lor c_1) & \land & (\lnot c_3 \lor c_2) & \land & (\lnot c_4 \lor c_3) & \land \\ (\lnot e_2 \lor e_1) & \land & (\lnot e_3 \lor e_2) & \land & (\lnot f_2 \lor f_1) & \land & (\lnot g_2 \lor g_1) & \land & (\lnot g_3 \lor g_2) & \land \\ (\lnot h_2 \lor h_1) & \land & (\lnot h_3 \lor h_2) & \land & (\lnot i_2 \lor i_1) & \land & (\lnot i_3 \lor i_2) & \land & (\lnot j_2 \lor j_1) & \land \\ (\lnot j_3 \lor j_2) & \land & (\lnot j_4 \lor j_3) & \land & (\lnot k_2 \lor k_1) & \land & (\lnot l_2 \lor l_1) & \land & (\lnot m_2 \lor m_1) & \land \\ (\lnot m_3 \lor m_2) & \land & (\lnot m_4 \lor m_3) & \land & (\lnot n_2 \lor n_1) & \land & (\lnot n_3 \lor n_2) & \land & (\lnot o_2 \lor o_1) & \land \\ (\lnot p_2 \lor p_1) & \land & (\lnot p_3 \lor p_2) & \land & (\lnot p_4 \lor p_3) & \land & (\lnot q_2 \lor q_1) & \land & (\lnot q_3 \lor q_2) & \land \\ (\lnot r_2 \lor r_1) & \land & (\lnot r_3 \lor r_2) & \land & (\lnot s_2 \lor s_1) & \land & (\lnot s_3 \lor s_2) & \land & (\lnot t_2 \lor t_1) & \land \\ (\lnot t_3 \lor t_2) & \land & (\lnot u_2 \lor u_{1a}) & \land & (\lnot u_2 \lor u_{1b}) & \land & (\lnot u_3 \lor u_2) & \land & (\lnot v_2 \lor v_1) & \land \\ (\lnot v_3 \lor v_2) & \land & (\lnot v_4 \lor v_3) & \land & (\lnot w_2 \lor w_1) & \land & (\lnot w_3 \lor w_2) & \land & (\lnot x_2 \lor x_1) & \land \\ (\lnot y_2 \lor y_1) & \land & (\lnot z_2 \lor z_1) & \land & (\lnot z_3 \lor z_2) & \land & (\lnot A_2 \lor A_1) & \land & (\lnot A_3 \lor A_2) & \land \\ (\lnot B_2 \lor B_1) & \land & (\lnot B_3 \lor B_2) & \land & (\lnot C_2 \lor C_1) & & & & & \\ & \\ \end{array}$$
Now, we should model the constraint for each row. For any given line with $x$ variables, there would be $2^x$ possible ways to value the variables. So, for the 1st and 12th rows there are 32 possible ways to choose the variables for each one. For the 4th row, there are 64 ways. For the 2nd, 5th, 6th, 7th and 10th rows there are 128 ways. For the 3rd, 9th and 11th rows there are 256 ways. For the 8th row there are 512 ways. However, only the ways that satisfy the given number for each line should be considered.
1st row: $$ \begin{array}{cccccccccccc} ( & z_3 & \land & C_2 & \land & \lnot A_3 & \land & \lnot D_1 & \land & \lnot B_3 & ) & \lor \\ ( & \lnot z_3 & \land & \lnot C_2 & \land & A_3 & \land & \lnot D_1 & \land & B_3 & ) & \lor \\ ( & \lnot z_3 & \land & \lnot C_2 & \land & \lnot A_3 & \land & D_1 & \land & \lnot B_3 & ) & \\ \end{array}$$
4th row: $$ \begin{array}{cccccccccccc} ( & u_2 & \land & s_3 & \land & \lnot w_1 & \land & \lnot t_3 & \land & \lnot x_1 & \land & \lnot v_2 & ) & \lor \\ ( & u_2 & \land & \lnot s_3 & \land & \lnot w_1 & \land & t_3 & \land & \lnot x_1 & \land & \lnot v_2 & ) & \lor \\ ( & u_2 & \land & \lnot s_3 & \land & \lnot w_1 & \land & \lnot t_3 & \land & \lnot x_1 & \land & v_2 & ) & \lor \\ ( & \lnot u_2 & \land & s_3 & \land & w_1 & \land & t_3 & \land & \lnot x_1 & \land & v_2 & ) & \lor \\ ( & \lnot u_2 & \land & s_3 & \land & \lnot w_1 & \land & t_3 & \land & x_1 & \land & \lnot v_2 & ) & \lor \\ ( & \lnot u_2 & \land & \lnot s_3 & \land & w_1 & \land & \lnot t_3 & \land & x_1 & \land & \lnot v_2 & ) & \lor \\ ( & \lnot u_2 & \land & \lnot s_3 & \land & \lnot w_1 & \land & t_3 & \land & x_1 & \land & v_2 & ) & \\ \end{array}$$
12th row: $$ \begin{array}{cccccccccccc} ( & a_1 & \land & \lnot b_1 & \land & c_1 & \land & d_1 & \land & \lnot e_1 & ) & \lor \\ ( & a_1 & \land & \lnot b_1 & \land & c_1 & \land & \lnot d_1 & \land & e_1 & ) & \lor \\ ( & \lnot a_1 & \land & b_1 & \land & \lnot c_1 & \land & d_1 & \land & \lnot e_1 & ) & \lor \\ ( & \lnot a_1 & \land & b_1 & \land & \lnot c_1 & \land & \lnot d_1 & \land & e_1 & ) & \\ \end{array}$$
Note: I did not modeled the other rows. Too tired.
For each column there are exact 12 variables, so we can value each column in 4096 different ways. Again, only a few satisfy the given numbers. Further, violations to the gravity constraints should obviously be discarded.
Note: I did not modeled the columns. Too tired.
AtIn the end we get a boolean formula like this:
$$\text{gravity constraints} \land \text{1st row constraints} \land \text{2nd row constraints} \land \text{3rd row constraints} \land \text{4th row constraints} \land \text{5th row constraints} \land \text{6th row constraints} \land \text{7th row constraints} \land \text{8th row constraints} \land \text{9th row constraints} \land \text{10th row constraints} \land \text{11th row constraints} \land \text{12th row constraints} \land \text{1st column constraints} \land \text{2nd column constraints} \land \text{3rd column constraints} \land \text{4th column constraints} \land \text{5th column constraints} \land \text{6th column constraints} \land \text{7th column constraints} \land \text{8th column constraints} \land \text{9th column constraints} \land \text{10th column constraints} \land \text{11th column constraints} \land \text{12th column constraints}$$
And then we will need to "just" solve that boolean formula.
To simplify the formula, at the 1st row, we can see that:
$z_3 = C_2$
$A_3 = B_3$
At the 12th row, we can see that:
$b_1 = \lnot a_1$
$c_1 = a_1$
$d_1 = \lnot e_1$
So, with this we can reduce the number of variables from 83 to 78.
Note: I will stop by now. Too tired.