Note: this is a list I made myself, so there may be things missing. I tried to include the most common situations, so don't take this as an exhaustive and fully comprehensive guide for when to use "de" and when to use "del" with compound names. That said, below is a list of situations when the article is required or not with some examples.
When speaking of materials:
- Mesa de madera (wooden table)
- Lata de hojalata (tin can)
- Escultura de hielo (ice sculpture)
- Abrigo de pelo (fur coat)
- Tarta de chocolate (chocolate cake)
- Salsa de gambas (shrimp sauce)
With seasons and months:
- Vestido de primavera/verano/otoño/invierno (spring/summer/autumn/winter dress)
- Primera quincena de febrero (first fortnight of February)
With a genre or theme:
- Película de terror (horror movie)
- Canción de amor (love song)
- Cine de autor (auteur cinema)
When speaking of emotional displays:
- Saltar de alegría (to jump with/for joy)
- Lágrimas de impotencia (tears of impotence)
- Ataque de ira (anger outburst)
- Mueca de dolor (wince)
Some fixed expressions:
- Fondo de armario (wardrobe basics; wardrobe essentials)
- Informe de errores (error report)
- Servicio de habitaciones (room service)
- Comida de empresa (business lunch; company lunch)
- Fiesta de despedida (farewell party)
- Bodas de oro (golden anniversary)
- Cuesta de enero (January’s uphill battle)
- Grito de guerra (war cry)
- Fin de semana (weekend)
When describing a part of something else:
- Pata de la mesa (table leg)
- Puerta de la cocina (kitchen door)
- Valle del río (river valley)
- Proa del barco (boat’s stern)
- Mango del cuchillo (knife handle)
- Prisas de los lunes (Monday rush)
- Bajón de los domingos (Sunday blues)
In many cases, an article is added in the situations in the first part when the noun is specified:
La primera quincena de Febrero es especialmente dura = the first fortnight of February is specially tough.
La primera quincena del Febrero de 1998 fue especialmente dura = the first fortnight of February 1998 was especially tough.
Similarly, in the first case of the second part (a part of something else), the article can be omitted when the noun is unspecific:
Una pata de mesa debe ser resistente = a table leg must be resistant.
La pata de la mesa de mi habitación es resistente = my room’s table leg is resistant.
However, this isn't always true: "valle de río" is always wrong, either if it is a specific valley or an unspecific one. When the article can be omitted and when not seems to be arbitrary, and hence dependant on each single case.
Finally, in your sentences "el suelo del bosque" fits into "a part of something else"; "el salto de agua" fits both in "materials" and "fixed expressions"; and "la copa del árbol" fits into "a part of something else".